Method and Apparatus for Measuring and Feeding Back Channel Information

ABSTRACT

and wherein Va0 and Va1 are elements in the vector Va, and Vb0 and Vb1 are elements in the vector Vb and sending a codebook index to a second network device, wherein the codebook index is associated with the first codebook selected from the first codebook set.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.15/700,909, filed on Sep. 11, 2017, which is a continuation of U.S.application Ser. No. 15/352,381, filed on Nov. 15, 2016, now U.S. Pat.No. 9,838,096, which is a continuation of International Application No.PCT/CN2014/077598, filed on May 15, 2014. All of the afore-mentionedpatent applications are hereby incorporated by reference in theirentireties.

TECHNICAL FIELD

Embodiments of the present invention relate to the communications field,and in particular, to MIMO coding and decoding technologies in an LTEsystem.

BACKGROUND

The multiple input multiple output (MIMO) technology is extensivelyapplied in wireless communications systems to increase system capacitiesand ensure cell coverage. For example, in a Long Term Evolution LTE)system, transmit diversity based on multiple antennas, open-loop orclosed-loop spatial multiplexing, and multi-stream transmission based ona demodulation reference signal (DM-RS) are used in a downlink. Amongthem, the DM-RS based multi-stream transmission is a main transmissionmode in an LTE-Advanced (LTE-A) system and later systems.

In a conventional cellular system, a beam at a transmit side of a basestation can be adjusted only in a horizontal dimension. In a verticaldimension, however, a fixed downtilt is used for every user. Therefore,various beamforming or precoding technologies or the like are all basedon channel information in the horizontal dimension. In practice,however, because a channel is three-dimensional (3D), the fixed downtiltmethod cannot always optimize a system throughput. Therefore, a beamadjustment in the vertical dimension is of great significance to systemperformance enhancement.

A conception of a 3D beamforming technology is mainly as follows: A 3Dbeamforming weighted vector at an active antenna side is adjustedaccording to 3D channel information estimated at a user side, so that amain lobe of a beam in a 3D space “aims at” a target user. In this way,received signal power is increased greatly, a signal to interferenceplus noise ratio is increased, and further, the throughput of the entiresystem is enhanced. Schematic diagrams of comparison between a dynamicdowntilt in 3D beamforming and a fixed downtilt of a conventionalantenna are shown in FIG. 1 and FIG. 2. An antenna port model with afixed downtilt is shown in FIG. 1, where corresponding to conventional2D MIMO, a fixed downtilt is used for all users. An antenna port modelwith a dynamic downtilt is shown in FIG. 2, where for each physicalresource block (PRB), a base station may dynamically adjust a downtiltaccording to a location of a served user. The 3D beamforming technologyneeds to be based on an active antenna system. Compared with aconventional antenna, the active antenna AAS further provides a degreeof freedom in a vertical direction. FIG. 3 shows a schematic diagram ofAAS antennas. It can be seen that there are multiple antennas in thevertical direction of AAS antennas. Therefore, a beam can be formed inthe vertical direction dynamically, and a degree of freedom ofbeamforming in the vertical direction is added. FIG. 4 shows a flowchartin which data is processed in baseband and radio frequency networks, andtransmitted through an AAS antenna. In a baseband processing part, adata stream at each layer undergoes precoding processing, and then ismapped to NP ports. After undergoing inverse fast Fourier transform(IFFT) and parallel-to-serial conversion, a data stream on each portenters a drive network in a radio frequency part, and then istransmitted through an antenna. Each drive network is a 1-to-M drivenetwork, that is, one port corresponds to M antenna elements. FIG. 5shows a schematic diagram of downtilt grouping. In the example, thereare eight antenna ports, and each port drives four antenna elements toform a downtilt. In addition, four antenna ports (ports 0 to 3) in ahorizontal direction have a same weighted vector in drive networks, andall point to a downtilt 0; the other four antenna ports (ports 4 to 7)have a same weighted vector, and all point to a downtilt 1.

In the prior art, spatially multiplexed multi-stream data can betransmitted only in a plane with a fixed downtilt by using a horizontalbeam, and characteristics of a vertical space cannot be used tomultiplex multiple data streams.

SUMMARY

In view of this, embodiments of the present invention provide a methodand an apparatus for measuring and feeding back channel information.

According to a first aspect, a method for measuring and feeding backchannel information is provided, including: receiving, by a firstnetwork device, a reference signal, measuring the reference signal toobtain a measurement result, and selecting a first codebook from a firstcodebook set according to the measurement result; where the firstcodebook set includes at least two first codebooks, a sub-vector W_(x)of each first codebook is formed by a zero vector and a non-zero vector,and the vectors forming the W_(x) correspond to different groups ofantenna ports; in each first codebook, different sub-vectors W_(x) areformed according to a same structure or different structures; formationaccording to the same structure is: for different sub-vectors W_(x)(1)and W_(x)(2), a location of a non-zero vector in the W_(x)(1) is thesame as a location of a non-zero vector in the W_(x)(2); and formationaccording to different structures is: for different sub-vectors W_(x)(1)and W_(x)(2), a location of a non-zero vector in the W_(x)(1) isdifferent from a location of a non-zero vector in the W_(x)(2); andsending a codebook index to a second network device, where the codebookindex corresponds to the first codebook selected from the first codebookset.

With reference to the first aspect, in a first possible implementationmanner, each first codebook includes at least one first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

having a first structure and/or at least one second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

having a second structure; where V_(a) in

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

is an n1-dimensional non-zero vector and corresponds to a first group ofantenna ports; 0 in

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

represents an n2-dimensional zero vector and corresponds to a secondgroup of antenna ports; V_(b) in

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

is an n2-dimensional non-zero vector and corresponds to the second groupof antenna ports; and 0 in

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

represents an n1-dimensional zero vector and corresponds to the firstgroup of antenna ports.

With reference to the first aspect, in a second possible implementationmanner, at least one first codebook meets a first condition, where thefirst condition is: a vector set formed by all first phase vectors and adiscrete Fourier transform matrix DFT matrix meet a first correspondencethat the vector set formed by the first phase vectors is a subset of aset of corresponding column vectors in a phase matrix of the DFT matrix,where an element in a P^(th) row and a Q^(th) column in the phase matrixof the DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the first phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding first phase vector, where P, Q, and K areany positive integers; or a vector set formed by all second phasevectors and at least one CMP codebook in a Cubic Metric Preserving (CMP)cubic metric preserving codebook set meet a second correspondence thatthe vector set formed by the second phase vectors is a subset of a setof corresponding column vectors in a phase matrix of the CMP codebookmatrix, where an element in a P^(th) row and a Q^(th) column in thephase matrix of the CMP codebook matrix is a phase part of an element ina P^(th) row and a Q^(th) column in the CMP codebook matrix, V_(a) partsof all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the second phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding second phase vector, where P, Q, and K areany positive integers; or a vector set formed by all third phase vectorsis a set formed by corresponding sub-vectors in a householder transformcodebook, where V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the third phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding third phase vector.

With reference to the first aspect, in a third possible implementationmanner, at least one first codebook meets a second condition, where thesecond condition is: a vector set formed by all fourth phase vectors anda discrete Fourier transform matrix DFT matrix meet a thirdcorrespondence that the vector set formed by the fourth phase vectors isa subset of a set of corresponding column vectors in a phase matrix ofthe DFT matrix, where an element in a P^(th) row and a Q^(th) column inthe phase matrix of the DFT matrix is a phase part of an element in aP^(th) row and a Q^(th) column in the DFT matrix, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fourth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fourth phase vector; or a vector setformed by all fifth phase vectors and at least one CMP codebook in a CMPcodebook set meet a fourth correspondence that the vector set formed bythe fifth phase vectors is a subset of a set of corresponding columnvectors in a phase matrix of the CMP codebook matrix, where an elementin a P^(th) row and a Q^(th) column in the phase matrix of the CMP is aphase part of an element in a P^(th) row and a Q^(th) column in the CMPcodebook matrix, V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fifth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fifth phase vector, where P, Q, and K areany positive integers; or a vector set formed by all sixth phase vectorsis a set formed by corresponding sub-vectors in a householder transformcodebook, where V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the sixth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding sixth phase vector.

With reference to the first aspect, in a fourth possible implementationmanner, at least one first codebook meets a third condition, where thethird condition is: in all first amplitude vectors corresponding to{V_(m)}, at least one first amplitude vector is different from allsecond amplitude vectors corresponding to the {V_(n)}; and/or in allsecond amplitude vectors corresponding to the {V_(n)}, at least onesecond amplitude vector is different from all first amplitude vectorscorresponding to the {V_(m)}; where V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form the set {V_(m)}, amplitude parts of allelements in each sub-vector of the {V_(m)} form the first amplitudevector, and a phase part of a K^(th) element in each sub-vector of the{V_(m)}is a K^(th) element of each corresponding first amplitude vector;and V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form the set {V_(n)}, amplitude parts of allelements in each sub-vector of the {V_(n)} form the second amplitudevector, and an amplitude part of a K^(th) element in each sub-vector ofthe {V_(n)} is a K^(th) element of each corresponding second amplitudevector.

With reference to the first aspect, in a fifth possible implementationmanner, the method includes: receiving at least one first configurationmessage, where each first configuration message is used to determine asub-vector set of phase parts corresponding to one group of antennaports, and a quantity of the at least one first configuration message isequal to a quantity of groups of the antenna ports; and/or receiving atleast one second configuration message, where each second configurationmessage is used to determine a sub-vector set of amplitude partscorresponding to one group of antenna ports, and a quantity of the atleast one second configuration message is equal to a quantity of groupsof the antenna ports.

With reference to the first aspect, in a sixth possible implementationmanner, the first configuration message is configured by the secondnetwork device by using higher layer signaling or dynamic signaling;and/or the second configuration message is configured by the secondnetwork device by using higher layer signaling or dynamic signaling.

With reference to the first aspect, in a seventh possible implementationmanner, the first configuration message is obtained by the first networkdevice by measuring the reference signal; and/or the secondconfiguration message is obtained by the first network device bymeasuring the reference signal.

With reference to the first aspect, in an eighth possible implementationmanner, the present invention provides different combinations in thefirst codebook matrix in different ranks.

With reference to the first aspect, in a ninth possible implementationmanner, when the value of the RI is greater than 1, V_(a) parts of allfirst sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in each first codebook form a sub-vector set {V_(K)}, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in each first codebook form a sub-vector set {V_(L)}, and thecorresponding {V_(K)} and {V_(L)} in the same first codebook meet afourth condition, where the fourth condition is: phase parts of asub-vector V_(k) in the {V_(k)} form a vector V_(k)′, vectors V_(k)′corresponding to all sub-vectors V_(k) in the {V_(k)} form a set{V_(k)′}, phase parts of a sub-vector V_(L) in the {V_(L)} form a vectorV_(L)′, vectors V_(L)′ corresponding to all sub-vectors V_(L) in the{V_(L)} form a set {V_(L)′}, and {V_(k′)}≠{V_(L)′} holds true.

With reference to the first aspect, in a tenth possible implementationmanner, when the value of the RI is greater than 1, V_(a) parts of allfirst sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in each first codebook form a sub-vector set {V_(M)}, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in each first codebook form a sub-vector set {V_(N)}, and thecorresponding {V_(M)} and {V_(N)} in the same first codebook meet afifth condition, where the fifth condition is: amplitude parts of asub-vector V_(M) in the {V_(M)} form a vector V_(M)′, vectors V_(M)′corresponding to all sub-vectors V_(M) in the {V_(M)} form a set{V_(M)′}, amplitude parts of a sub-vector V_(N) in the {V_(N)} form avector V_(N)′, vectors V_(N)′ corresponding to all sub-vectors V_(N) inthe {V_(N)} form a set {V_(N)′}, and {V_(M)′}≠{V_(N)′} holds true.

With reference to the first aspect, in an eleventh possibleimplementation manner, at least two elements in an amplitude vector inV_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are unequal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are unequal; or at least two elements in anamplitude vector in V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are unequal, and all elements in an amplitudevector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are equal; or all elements in an amplitude vectorin V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are equal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are unequal.

With reference to the first aspect, in a twelfth possible implementationmanner, at least two amplitude vectors in a vector set formed byamplitude vectors in V_(a) of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are different; or at least two amplitude vectorsin a vector set formed by amplitude vectors in V_(b) of all secondsub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are different.

With reference to the first aspect, in a thirteenth possibleimplementation manner, the first network device is a terminal device UE.

With reference to the first aspect, in a fourteenth possibleimplementation manner, the second network device is a base station eNB.

According to a second aspect, a method for measuring and feeding backchannel information is provided, including: sending a reference signalto a first network device, where the reference signal is used to notifythe first network device to perform a measurement to obtain ameasurement result; receiving a codebook index sent by the first networkdevice, where the codebook index corresponds to a first codebookdetermined in the first codebook set by the first network device, andthe codebook index is determined by the first network device accordingto the measurement result; where the first codebook set includes atleast two first codebooks, a sub-vector W_(x) of each first codebook isformed by a zero vector and a non-zero vector, and the vectors formingthe W_(x) correspond to different groups of antenna ports; in each firstcodebook, different sub-vectors W_(x) are formed according to a samestructure or different structures; formation according to the samestructure is: for different sub-vectors W_(x)(1) and W_(x)(2), alocation of a non-zero vector in the W_(x)(1) is the same as a locationof a non-zero vector in the W_(x)(2); and formation according todifferent structures is: for different sub-vectors W_(x)(1) andW_(x)(2), a location of a non-zero vector in the W_(x)(1) is differentfrom a location of a non-zero vector in the W_(x)(2); and determining,according to the codebook index, the first codebook determined in thefirst codebook set by the first network device.

With reference to the second aspect, in a first possible implementationmanner, each first codebook includes at least one first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

having a first structure and/or at least one second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

having a second structure; where V_(a) in

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

is an n1-dimensional non-zero vector and corresponds to a first group ofantenna ports; 0 in

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

represents an n2-dimensional zero vector and corresponds to a secondgroup of antenna ports; V_(b) in

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

is an n2-dimensional non-zero vector and corresponds to the second groupof antenna ports; and 0 in

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

represents an n1-dimensional zero vector and corresponds to the firstgroup of antenna ports.

With reference to the second aspect, in a second possible implementationmanner, at least one first codebook meets a first condition, where thefirst condition is: a vector set formed by all first phase vectors and adiscrete Fourier transform matrix DFT matrix meet a first correspondencethat the vector set formed by the first phase vectors is a subset of aset of corresponding column vectors in a phase matrix of the DFT matrix,where an element in a P^(th) row and a Q^(th) column in the phase matrixof the DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the first phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding first phase vector, where P, Q, and K areany positive integers; or a vector set formed by all second phasevectors and at least one CMP codebook in a CMP codebook set meet asecond correspondence that the vector set formed by the second phasevectors is a subset of a set of corresponding column vectors in a phasematrix of the CMP codebook matrix, where an element in a P^(th) row anda Q^(th) column in the phase matrix of the CMP codebook matrix is aphase part of an element in a P^(th) row and a Q^(th) column in the CMPcodebook matrix, V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the second phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding second phase vector, where P, Q, and K areany positive integers; or a vector set formed by all third phase vectorsis a set formed by corresponding sub-vectors in a householder transformcodebook, where V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the third phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding third phase vector.

With reference to the second aspect, in a third possible implementationmanner, at least one first codebook meets a second condition, where thesecond condition is: a vector set formed by all fourth phase vectors anda discrete Fourier transform matrix DFT matrix meet a thirdcorrespondence that the vector set formed by the fourth phase vectors isa subset of a set of corresponding column vectors in a phase matrix ofthe DFT matrix, where an element in a P^(th) row and a Q^(th) column inthe phase matrix of the DFT matrix is a phase part of an element in aP^(th) row and a Q^(th) column in the DFT matrix, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fourth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fourth phase vector; or a vector setformed by all fifth phase vectors and at least one CMP codebook in a CMPcodebook set meet a fourth correspondence that the vector set formed bythe fifth phase vectors is a subset of a set of corresponding columnvectors in a phase matrix of the CMP codebook matrix, where an elementin a P^(th) row and a Q^(th) column in the phase matrix of the CMP is aphase part of an element in a P^(th) row and a Q^(th) column in the CMPcodebook matrix, V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fifth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fifth phase vector, where P, Q, and K areany positive integers; or a vector set formed by all sixth phase vectorsis a set formed by corresponding sub-vectors in a householder transformcodebook, where V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the sixth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding sixth phase vector.

With reference to the second aspect, in a fourth possible implementationmanner, at least one first codebook meets a third condition, where thethird condition is: in all first amplitude vectors corresponding to{V_(m)}, at least one first amplitude vector is different from allsecond amplitude vectors corresponding to the {V_(n)}; and/or in allsecond amplitude vectors corresponding to the {V_(n)}, at least onesecond amplitude vector is different from all first amplitude vectorscorresponding to the {V_(m)}; where V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form the set {V_(m)}, amplitude parts of allelements in each sub-vector of the {V_(m)} form the first amplitudevector, and a phase part of a K^(th) element in each sub-vector of the{V_(m)} is a K^(th) element of each corresponding first amplitudevector; and V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form the set {V_(n)}, amplitude parts of allelements in each sub-vector of the {V_(n)} form the second amplitudevector, and an amplitude part of a K^(th) element in each sub-vector ofthe {V_(n)} is a K^(th) element of each corresponding second amplitudevector.

With reference to the second aspect, in a fifth possible implementationmanner, the method includes: sending at least one first configurationmessage to the first network device, where each first configurationmessage is used to determine a sub-vector set of phase partscorresponding to one group of antenna ports, and a quantity of the atleast one first configuration message is equal to a quantity of groupsof the antenna ports; and/or sending at least one second configurationmessage to the first network device, where each second configurationmessage is used to determine a sub-vector set of amplitude partscorresponding to one group of antenna ports, and a quantity of the atleast one second configuration message is equal to a quantity of groupsof the antenna ports.

With reference to the second aspect, in a sixth possible implementationmanner, the first configuration message is configured by a secondnetwork device by using higher layer signaling or dynamic signaling;and/or the second configuration message is configured by a secondnetwork device by using higher layer signaling or dynamic signaling.

With reference to the second aspect, in a seventh possibleimplementation manner, the reference signal is further used to indicatethe first configuration message; and/or the reference signal is furtherused to indicate the second configuration message.

With reference to the second aspect, in an eighth possibleimplementation manner, the present invention provides differentcombinations in the first codebook matrix in different ranks.

With reference to the second aspect, in a ninth possible implementationmanner, when the value of the RI is greater than 1, V_(a) parts of allfirst sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in each first codebook form a sub-vector set {V_(K)}, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in each first codebook form a sub-vector set {V_(L)}, and thecorresponding {V_(K)} and {V_(L)} in the same first codebook meet afourth condition, where the fourth condition is: phase parts of asub-vector V_(k) in the {V_(k)} form a vector V_(k)′, vectors V_(k)′corresponding to all sub-vectors V_(k) in the {V_(k)} form a set{V_(k)′}, phase parts of a sub-vector V_(L) in the {V_(L)} form a vectorV_(L)′, vectors V_(L)′ corresponding to all sub-vectors V_(L) in the{V_(L)} form a set {V_(L)′}, and {V_(k)′}≠{V_(L)′} holds true.

With reference to the second aspect, in a tenth possible implementationmanner, when the value of the RI is greater than 1, V_(a) parts of allfirst sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in each first codebook form a sub-vector set {V_(M)}, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in each first codebook form a sub-vector set {V_(N)}, and thecorresponding {V_(M)} and {V_(N)} in the same first codebook meet afifth condition, where the fifth condition is: amplitude parts of asub-vector V_(M) in the {V_(M)} form a vector V_(M)′, vectors V_(M)′corresponding to all sub-vectors V_(M) in the {V_(M)} form a set{V_(M)′}, amplitude parts of a sub-vector V_(N) in the {V_(N)} form avector V_(N)′, vectors V_(N)′ corresponding to all sub-vectors V_(N) inthe {V_(N)} form a set {V_(N)′}, and {V_(M)′}≠{V_(N)′} holds true.

With reference to the second aspect, in an eleventh possibleimplementation manner, at least two elements in an amplitude vector inV_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are unequal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are unequal; or at least two elements in anamplitude vector in V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are unequal, and all elements in an amplitudevector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are equal; or all elements in an amplitude vectorin V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are equal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are unequal.

With reference to the second aspect, in a twelfth possibleimplementation manner, at least two amplitude vectors in a vector setformed by amplitude vectors in V_(a) of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are different; or at least two amplitude vectorsin a vector set formed by amplitude vectors in V_(b) of all secondsub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are different.

With reference to the second aspect, in a thirteenth possibleimplementation manner, the first network device is a terminal device UE.

With reference to the second aspect, in a fourteenth possibleimplementation manner, the second network device is a base station eNB.

According to a third aspect, an apparatus for measuring and feeding backchannel information is provided, including: a first receiving unit,configured to receive a reference signal; a measurement unit, configuredto measure the reference signal to obtain a measurement result; aselection unit, configured to select a first codebook from a firstcodebook set according to the measurement result; where the firstcodebook set includes at least two first codebooks, a sub-vector W_(x)of each first codebook is formed by a zero vector and a non-zero vector,and the vectors forming the W_(x) correspond to different groups ofantenna ports; in each first codebook, different sub-vectors W_(x) areformed according to a same structure or different structures; formationaccording to the same structure is: for different sub-vectors W_(x)(1)and W_(x)(2), a location of a non-zero vector in the W_(x)(1) is thesame as a location of a non-zero vector in the W_(x)(2); and formationaccording to different structures is: for different sub-vectors W_(x)(1)and W_(x)(2), a location of a non-zero vector in the W_(x)(1) isdifferent from a location of a non-zero vector in the W_(x)(2); and asending unit, configured to send a codebook index to a second networkdevice, where the codebook index corresponds to the first codebookselected from the first codebook set.

With reference to the third aspect, in a first possible implementationmanner, each first codebook includes at least one first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

having a first structure and/or at least one second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

having a second structure; where V_(a) in

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

is an n1-dimensional non-zero vector and corresponds to a first group ofantenna ports; 0 in

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

represents an n2-dimensional zero vector and corresponds to a secondgroup of antenna ports; V_(b) in

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

is an n2-dimensional non-zero vector and corresponds to the second groupof antenna ports; and 0 in

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

represents an n1-dimensional zero vector and corresponds to the firstgroup of antenna ports.

With reference to the third aspect, in a second possible implementationmanner, at least one first codebook meets a first condition, where thefirst condition is: a vector set formed by all first phase vectors and adiscrete Fourier transform matrix DFT matrix meet a first correspondencethat the vector set formed by the first phase vectors is a subset of aset of corresponding column vectors in a phase matrix of the DFT matrix,where an element in a P^(th) row and a Q^(th) column in the phase matrixof the DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the first phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding first phase vector, where P, Q, and K areany positive integers; or a vector set formed by all second phasevectors and at least one CMP codebook in a CMP codebook set meet asecond correspondence that the vector set formed by the second phasevectors is a subset of a set of corresponding column vectors in a phasematrix of the CMP codebook matrix, where an element in a P^(th) row anda Q^(th) column in the phase matrix of the CMP codebook matrix is aphase part of an element in a P^(th) row and a Q^(th) column in the CMPcodebook matrix, V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the second phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding second phase vector, where P, Q, and K areany positive integers; or a vector set formed by all third phase vectorsis a set formed by corresponding sub-vectors in a householder transformcodebook, where V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the third phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding third phase vector.

With reference to the third aspect, in a third possible implementationmanner, at least one first codebook meets a second condition, where thesecond condition is: a vector set formed by all fourth phase vectors anda discrete Fourier transform matrix DFT matrix meet a thirdcorrespondence that the vector set formed by the fourth phase vectors isa subset of a set of corresponding column vectors in a phase matrix ofthe DFT matrix, where an element in a P^(th) row and a Q^(th) column inthe phase matrix of the DFT matrix is a phase part of an element in aP^(th) row and a Q^(th) column in the DFT matrix, V_(b) parts of allsecond sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fourth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fourth phase vector; or a vector setformed by all fifth phase vectors and at least one CMP codebook in a CMPcodebook set meet a fourth correspondence that the vector set formed bythe fifth phase vectors is a subset of a set of corresponding columnvectors in a phase matrix of the CMP codebook matrix, where an elementin a P^(th) row and a Q^(th) column in the phase matrix of the CMP is aphase part of an element in a P^(th) row and a Q^(th) column in the CMPcodebook matrix, V_(b) parts of all second sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fifth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fifth phase vector, where P, Q, and K areany positive integers; or a vector set formed by all sixth phase vectorsis a set formed by corresponding sub-vectors in a householder transformcodebook, where V_(b) parts of all second sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the sixth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding sixth phase vector.

With reference to the third aspect, in a fourth possible implementationmanner, at least one first codebook meets a third condition, where thethird condition is: in all first amplitude vectors corresponding to{V_(m)}, at least one first amplitude vector is different from allsecond amplitude vectors corresponding to the {V_(n)}; and/or in allsecond amplitude vectors corresponding to the {V_(n)}, at least onesecond amplitude vector is different from all first amplitude vectorscorresponding to the {V_(m)}; where V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form the set {V_(m)}, amplitude parts of allelements in each sub-vector of the {V_(m)} form the first amplitudevector, and a phase part of a K^(th) element in each sub-vector of the{V_(m)} is a K^(th) element of each corresponding first amplitudevector; and V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{a}\end{bmatrix}$

in the first codebook form the set {V_(n)}, amplitude parts of allelements in each sub-vector of the {V_(n)} form the second amplitudevector, and an amplitude part of a K^(th) element in each sub-vector ofthe {V_(n)} is a K^(th) element of each corresponding second amplitudevector.

With reference to the third aspect, in a fifth possible implementationmanner, the apparatus includes: a second receiving unit, configured toreceive at least one first configuration message, where each firstconfiguration message is used to determine a sub-vector set of phaseparts corresponding to one group of antenna ports, and a quantity of theat least one first configuration message is equal to a quantity ofgroups of the antenna ports; and/or a third receiving unit, configuredto receive at least one second configuration message, where each secondconfiguration message is used to determine a sub-vector set of amplitudeparts corresponding to one group of antenna ports, and a quantity of theat least one second configuration message is equal to a quantity ofgroups of the antenna ports.

With reference to the third aspect, in a sixth possible implementationmanner, the first configuration message is configured by the secondnetwork device by using higher layer signaling or dynamic signaling;and/or the second configuration message is configured by the secondnetwork device by using higher layer signaling or dynamic signaling.

With reference to the third aspect, in a seventh possible implementationmanner, the apparatus includes: a first acquiring unit, configured toacquire the first configuration message according to the result that isobtained by the measurement unit by measuring the reference signal;and/or a second acquiring unit, configured to acquire the secondconfiguration message according to the result that is obtained by themeasurement unit by measuring the reference signal.

With reference to the third aspect, in an eighth possible implementationmanner, the present invention provides different combinations in thefirst codebook matrix in different ranks.

With reference to the third aspect, in a ninth possible implementationmanner, when the value of the RI is greater than 1, V_(a) parts of allfirst sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in each first codebook form a sub-vector set {V_(K)}, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in each first codebook form a sub-vector set {V_(L)}, and thecorresponding {V_(K)} and {V_(L)} in the same first codebook meet afourth condition, where the fourth condition is: phase parts of asub-vector V_(k) in the {V_(k)} form a vector V_(k)′, vectors V_(k)′corresponding to all sub-vectors V_(k) in the {V_(k)} form a set{V_(k)′}, phase parts of a sub-vector V_(L) in the {V_(L)} form a vectorV_(L)′, vectors V_(L)′ corresponding to all sub-vectors V_(L) in the{V_(L)} form a set {V_(L)′}, and {V_(k)′}≠{V_(L)′} holds true.

With reference to the third aspect, in a tenth possible implementationmanner, when the value of the RI is greater than 1, V_(a) parts of allfirst sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in each first codebook form a sub-vector set {V_(M)}, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in each first codebook form a sub-vector set {V_(N)}, and thecorresponding {V_(M)} and {V_(N)} in the same first codebook meet afifth condition, where the fifth condition is: amplitude parts of asub-vector V_(M) in the {V_(M)} form a vector V_(M)′, vectors V_(M)′corresponding to all sub-vectors V_(M) in the {V_(M)} form a set{V_(M)′}, amplitude parts of a sub-vector V_(N) in the {V_(N)} form avector V_(N)′, vectors V_(N)′ corresponding to all sub-vectors V_(N) inthe {V_(N)} form a set {V_(N)′}, and {V_(M)′}≠{V_(N)′} holds true.

With reference to the third aspect, in an eleventh possibleimplementation manner, at least two elements in an amplitude vector inV_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are unequal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are unequal; or at least two elements in anamplitude vector in V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are unequal, and all elements in an amplitudevector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are equal; or all elements in an amplitude vectorin V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are equal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are unequal.

With reference to the third aspect, in a twelfth possible implementationmanner, at least two amplitude vectors in a vector set formed byamplitude vectors in V_(a) of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are different; or at least two amplitude vectorsin a vector set formed by amplitude vectors in of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are different.

With reference to the third aspect, in a thirteenth possibleimplementation manner, the first network device is a terminal device UE.

With reference to the third aspect, in a fourteenth possibleimplementation manner, the second network device is a base station eNB.

According to a fourth aspect, a communications apparatus is provided,including: a first sending unit, configured to send a reference signalto a first network device, where the reference signal is used to notifythe first network device to perform a measurement to obtain ameasurement result; a receiving unit, configured to receive a codebookindex sent by the first network device, where the codebook indexcorresponds to a first codebook determined in the first codebook set bythe first network device, and the codebook index is determined by thefirst network device according to the measurement result; and adetermining unit, configured to determine, according to the codebookindex, the first codebook in the first codebook set; where the firstcodebook set includes at least two first codebooks, a sub-vector W_(x)of each first codebook is formed by a zero vector and a non-zero vector,and the vectors forming the W_(x) correspond to different groups ofantenna ports; in each first codebook, different sub-vectors W_(x) areformed according to a same structure or different structures; formationaccording to the same structure is: for different sub-vectors W_(x)(1)and W_(x)(2), a location of a non-zero vector in the W_(x)(1) is thesame as a location of a non-zero vector in the W_(x)(2); and formationaccording to different structures is: for different sub-vectors W_(x)(1)and W_(x)(2), a location of a non-zero vector in the W_(x)(1) isdifferent from a location of a non-zero vector in the W_(x)(2).

With reference to the fourth aspect, in a first possible implementationmanner, each first codebook includes at least one first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

having a first structure and/or at least one second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

having a second structure; where V_(a) in

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

is an n1-dimensional non-zero vector and corresponds to a first group ofantenna ports; 0 in

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

represents an n2-dimensional zero vector and corresponds to a secondgroup of antenna ports; V_(b) in

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

is an n2-dimensional non-zero vector and corresponds to the second groupof antenna ports; and 0 in

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

represents an n1-dimensional zero vector and corresponds to the firstgroup of antenna ports.

With reference to the fourth aspect, in a second possible implementationmanner, at least one first codebook meets a first condition, where thefirst condition is: a vector set formed by all first phase vectors and adiscrete Fourier transform matrix DFT matrix meet a first correspondencethat the vector set formed by the first phase vectors is a subset of aset of corresponding column vectors in a phase matrix of the DFT matrix,where an element in a P^(th) row and a Q^(th) column in the phase matrixof the DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the first phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding first phase vector, where P, Q, and K areany positive integers; or a vector set formed by all second phasevectors and at least one CMP codebook in a CMP codebook set meet asecond correspondence that the vector set formed by the second phasevectors is a subset of a set of corresponding column vectors in a phasematrix of the CMP codebook matrix, where an element in a P^(th) row anda Q^(th) column in the phase matrix of the CMP codebook matrix is aphase part of an element in a P^(th) row and a Q^(th) column in the CMPcodebook matrix, V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the second phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding second phase vector, where P, Q, and K areany positive integers; or a vector set formed by all third phase vectorsis a set formed by corresponding sub-vectors in a householder transformcodebook, where V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the third phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding third phase vector.

With reference to the fourth aspect, in a third possible implementationmanner, at least one first codebook meets a second condition, where thesecond condition is: a vector set formed by all fourth phase vectors anda discrete Fourier transform matrix DFT matrix meet a thirdcorrespondence that the vector set formed by the fourth phase vectors isa subset of a set of corresponding column vectors in a phase matrix ofthe DFT matrix, where an element in a P^(th) row and a Q^(th) column inthe phase matrix of the DFT matrix is a phase part of an element in aP^(th) row and a Q^(th) column in the DFT matrix, V_(b) parts of allsecond sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fourth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fourth phase vector; or a vector setformed by all fifth phase vectors and at least one CMP codebook in a CMPcodebook set meet a fourth correspondence that the vector set formed bythe fifth phase vectors is a subset of a set of corresponding columnvectors in a phase matrix of the CMP codebook matrix, where an elementin a P^(th) row and a Q^(th) column in the phase matrix of the CMP is aphase part of an element in a P^(th) row and a Q^(th) column in the CMPcodebook matrix, V_(b) parts of all second sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fifth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fifth phase vector, where P, Q, and K areany positive integers; or a vector set formed by all sixth phase vectorsis a set formed by corresponding sub-vectors in a householder transformcodebook, where V_(b) parts of all second sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the sixth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding sixth phase vector.

With reference to the fourth aspect, in a fourth possible implementationmanner, at least one first codebook meets a third condition, where thethird condition is: in all first amplitude vectors corresponding to{V_(m)}, at least one first amplitude vector is different from allsecond amplitude vectors corresponding to the {V_(n)}; and/or in allsecond amplitude vectors corresponding to the {V_(n)}, at least onesecond amplitude vector is different from all first amplitude vectorscorresponding to the {V_(m)}; where V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form the set {V_(m)}, amplitude parts of allelements in each sub-vector of the {V_(m)} form the first amplitudevector, and a phase part of a K^(th) element in each sub-vector of the{V_(m)} is a K^(th) element of each corresponding first amplitudevector; and V_(b) parts of all second sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form the set {V_(n)}, amplitude parts of allelements in each sub-vector of the {V_(n)} form the second amplitudevector, and an amplitude part of a K^(th) element in each sub-vector ofthe {V_(n)} is a K^(th) element of each corresponding second amplitudevector.

With reference to the fourth aspect, in a fifth possible implementationmanner, the apparatus includes: a second sending unit, configured tosend at least one first configuration message to the first networkdevice, where each first configuration message is used to determine asub-vector set of phase parts corresponding to one group of antennaports, and a quantity of the at least one first configuration message isequal to a quantity of groups of the antenna ports; and/or a thirdsending unit, configured to send at least one second configurationmessage to the first network device, where each second configurationmessage is used to determine a sub-vector set of amplitude partscorresponding to one group of antenna ports, and a quantity of the atleast one second configuration message is equal to a quantity of groupsof the antenna ports.

With reference to the fourth aspect, in a sixth possible implementationmanner, the second sending unit sends the first configuration message byusing higher layer signaling or dynamic signaling; and/or the thirdsending unit sends the second configuration message by using higherlayer signaling or dynamic signaling.

With reference to the fourth aspect, in a seventh possibleimplementation manner, the reference signal is further used to indicatethe at least one first configuration message, where each firstconfiguration message is used to determine a sub-vector set of phaseparts corresponding to one group of antenna ports, and a quantity of theat least one first configuration message is equal to a quantity ofgroups of the antenna ports; and/or the reference signal is further usedto indicate the at least one second configuration message, where eachsecond configuration message is used to determine a sub-vector set ofamplitude parts corresponding to one group of antenna ports, and aquantity of the at least one second configuration message is equal to aquantity of groups of the antenna ports.

With reference to the fourth aspect, in an eighth possibleimplementation manner, the present invention provides differentcombinations in the first codebook matrix in different ranks.

With reference to the fourth aspect, in a ninth possible implementationmanner, when the value of the RI is greater than 1, V_(a) parts of allfirst sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(K)}, V_(b) parts of allsecond sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(L)}, and thecorresponding {V_(K)} and {V_(L)} in the same first codebook meet afourth condition, where the fourth condition is: phase parts of asub-vector V_(k) in the {V_(k)} form a vector V_(k)′, vectors V_(k)′corresponding to all sub-vectors V_(k) in the {V_(k)} form a set{V_(k)′}, phase parts of a sub-vector V_(L) in the {V_(L)} form a vectorV_(L)′, vectors V_(L)′ corresponding to all sub-vectors V_(L) in the{V_(L)} form a set {V_(L)′}, and {V_(k)′}≠{V_(L)′} holds true.

With reference to the fourth aspect, in a tenth possible implementationmanner, when the value of the RI is greater than 1, V_(a) parts of allfirst sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(M)}, V_(b) parts of allsecond sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(N)}, and thecorresponding {V_(M)} and {V_(N)} in the same first codebook meet afifth condition, where the fifth condition is: amplitude parts of asub-vector V_(M) in the {V_(M)} form a vector V_(M)′, vectors V_(M)′corresponding to all sub-vectors V_(M) in the {V_(M)} form a set{V_(M)′}, amplitude parts of a sub-vector V_(N) in the {V_(N)} form avector V_(N)′, vectors V_(N)′ corresponding to all sub-vectors V_(N) inthe {V_(N)} form a set {V_(N)′}, and {V_(M)′}≠{V_(N)′} holds true.

With reference to the fourth aspect, in an eleventh possibleimplementation manner, at least two elements in an amplitude vector inV_(a) of each first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are unequal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are unequal; or at least two elements in anamplitude vector in V_(a) of each first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are unequal, and all elements in an amplitudevector in V_(b) of each second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are equal; or all elements in an amplitude vectorin V_(a) of each first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are equal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are unequal.

With reference to the fourth aspect, in a twelfth possibleimplementation manner, at least two amplitude vectors in a vector setformed by amplitude vectors in V_(a) of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are different; or at least two amplitude vectorsin a vector set formed by amplitude vectors in V_(b) of all secondsub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are different.

With reference to the fourth aspect, in a thirteenth possibleimplementation manner, the first network device is a terminal device UE.

With reference to the fourth aspect, in a fourteenth possibleimplementation manner, the second network device is a base station eNB.

In the foregoing solutions, a codebook structure provided by the presentinvention may be configured independently according to transmit power ofdifferent groups of antenna ports, so that flexibility and MIMOperformance are improved.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an architecture diagram of an antenna port model with a fixeddowntilt;

FIG. 2 is an architecture diagram of an antenna port model with adynamic downtilt;

FIG. 3 is a schematic diagram of an active antenna system AAS;

FIG. 4 is a flowchart in which data is processed in baseband and radiofrequency networks, and transmitted through an AAS antenna;

FIG. 5 is a schematic diagram of downtilt grouping;

FIG. 6 is a flowchart for implementing a method for measuring andfeeding back channel information by a first network device according tothe present invention;

FIG. 7 is a flowchart for implementing a method for measuring andfeeding back channel information by a second network device according tothe present invention;

FIG. 8 is a first schematic structural diagram of a network device forimplementing a method for measuring and feeding back channel informationaccording to the present invention;

FIG. 9 is a second schematic structural diagram of a network device forimplementing a method for measuring and feeding back channel informationaccording to the present invention;

FIG. 10 is a third schematic structural diagram of a network device forimplementing a method for measuring and feeding back channel informationaccording to the present invention;

FIG. 11 is a fourth schematic structural diagram of a network device forimplementing a method for measuring and feeding back channel informationaccording to the present invention;

FIG. 12 is a fifth schematic structural diagram of a network device forimplementing a method for measuring and feeding back channel informationaccording to the present invention;

FIG. 13 is a sixth schematic structural diagram of a network device forimplementing a method for measuring and feeding back channel informationaccording to the present invention;

FIG. 14 is a seventh schematic structural diagram of a network devicefor implementing a method for measuring and feeding back channelinformation according to the present invention;

FIG. 15 is an eighth schematic structural diagram of a network devicefor implementing a method for measuring and feeding back channelinformation according to the present invention;

FIG. 16 is a flowchart in a network system for implementing a method formeasuring and feeding back channel information according to the presentinvention; and

FIG. 17 is a structural diagram of a network device for implementing amethod for measuring and feeding back channel information according tothe present invention.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

For convenience, in the present invention, Table 1 to Table 6 arepresented repeatedly in the specification, and tables with a same numbercorrespond to same table content.

FIG. 6 shows a flowchart of a method embodiment according to the presentinvention, which is specifically as follows:

Step 101: A first network device receives a reference signal, measuresthe reference signal to obtain a measurement result, and selects a firstcodebook from a first codebook set according to the measurement result.

The first codebook set includes at least two first codebooks. Asub-vector W_(x) of each first codebook is formed by a zero vector and anon-zero vector, and the vectors forming the W_(x) correspond todifferent groups of antenna ports; in each first codebook, differentsub-vectors W_(x) are formed according to a same structure or differentstructures; formation according to the same structure is: for differentsub-vectors W_(x)(1) and W_(x)(2), a location of a non-zero vector inthe W_(x)(1) is the same as a location of a non-zero vector in theW_(x)(2); and formation according to different structures is: fordifferent sub-vectors W_(x)(1) and W_(x)(2), a location of a non-zerovector in the W_(x)(1) is different from a location of a non-zero vectorin the W_(x)(2).

Step 102: the first network device send a codebook index to a secondnetwork device, where the codebook index corresponds to the firstcodebook selected from the first codebook set.

It should be understood that, in the present invention, a zero vectormay be a zero element with a length of 1, and a non-zero vector may be anon-zero element with a length of 1. Generally, for a passive antenna, adowntilt in a vertical direction is fixed. Therefore, for multiplespatially multiplexed data streams, adjustments can be made to multiplehorizontal beams only in a plane with a fixed downtilt in the verticaldirection, and the multiple data streams cannot be multiplexed morefreely in planes with multiple downtilts. In addition, if antenna portsare grouped according to different downtilts, a codebook structureprovided by the present invention may be configured independentlyaccording to transmit power of different groups of antenna ports, sothat flexibility and MIMO performance are improved.

In an embodiment of the present invention, when antenna ports aregrouped according to tilts in the vertical direction, parameters ofcodebook vectors in a codebook may be configured independently accordingto different tilts, so that an objective of flexibly adapting to datatransmission efficiency is achieved. In this embodiment, two tilts inthe vertical direction are used as an example (this method is alsoapplicable to more than two tilts). In each column in the firstcodebook, one group of antenna ports corresponds to a non-zero vector,and another group of antenna ports corresponds to a zero vector; or onegroup of antenna ports corresponds to a zero vector, and another groupof antenna ports corresponds to a non-zero vector, where the non-zerovector refers to a vector in which at least one element is a non-zeroelement, and the zero vector refers to a vector in which all elementsare zero elements. In the present invention, when first n1 elements in avector included in a codebook correspond to one group of antenna ports,and last n2 elements correspond to another group of antenna ports, astructure of this vector is

$\begin{bmatrix}V_{1} \\V_{2}\end{bmatrix},$

where V₁ is n1-dimensional, and V₂ is n2-dimensional. In this case, eachfirst codebook includes at least one first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

having a first structure and/or at least one second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

having a second structure; where V_(a) in

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

is an n1-dimensional non-zero vector and corresponds to a first group ofantenna ports; 0 in

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

represents an n2-dimensional zero vector and corresponds to a secondgroup of antenna ports; V_(b) in

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

is an n2-dimensional non-zero vector and corresponds to the second groupof antenna ports; and 0 in

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

represents an n1-dimensional zero vector and corresponds to the firstgroup of antenna ports. It should be understood that, the presentinvention is not limited to the case of grouping into only two groups.In an actual application, antenna ports are grouped into more groupsaccording to other factors such as different downtilts or signal qualityor the like. In a specific measurement process, codebooks in the firstcodebook set are traversed, so that a first codebook that best matches atransmission characteristic is determined and used for channeltransmission.

It should be understood that, the structure of the sub-vector in thefirst codebook may be but is not limited to the foregoing firststructure or the second structure. Optionally, locations of sub-vectorsof the zero vector and the non-zero vector in the first codebook may bedifferent. In an embodiment of the present invention, in a case of fourantenna ports, elements in vectors in the first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

having the first structure are represented as

$\begin{bmatrix}V_{a}^{0} \\V_{a}^{1} \\0 \\0\end{bmatrix},$

and elements in vectors in the second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

having the second structure are represented as

$\begin{bmatrix}0 \\0 \\V_{b}^{0} \\V_{b}^{1}\end{bmatrix}{\quad,}$

where V_(a) ⁰ and V_(a) ¹ are elements in the vector V_(a), and V_(b) ⁰and V_(b) ¹ are elements in the vector V_(b). In another embodiment ofthe present invention, when the antenna ports are grouped into twogroups, the first structure may be

$\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix},$

and the second structure may be

$\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix}{\quad.}$

Likewise, when the antenna groups are grouped into two groups, inanother embodiment of the present invention, the first structure may be

$\begin{bmatrix}V_{a}^{0} \\0 \\0 \\V_{a}^{1}\end{bmatrix},$

and the second structure may be

$\begin{bmatrix}0 \\V_{b}^{0} \\V_{b}^{1} \\0\end{bmatrix}.$

Alternatively, the first codebook set includes at least one of thefollowing four structures: a first structure

$\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix},$

a second structure

$\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix},$

a third structure

$\begin{bmatrix}V_{a}^{0} \\0 \\0 \\V_{a}^{1}\end{bmatrix},$

or a fourth structure

$\begin{bmatrix}0 \\V_{b}^{0} \\V_{b}^{1} \\0\end{bmatrix}.$

V_(a) ⁰ and V_(a) ¹ are elements in the vector V_(a), and Va correspondsto one group of antenna ports. A correspondence is as follows: In thefirst structure, V_(a) ⁰ corresponds to a first antenna port, and V_(a)¹ corresponds to a third antenna port; in the second structure, V_(b) ⁰corresponds to a second antenna port, and V_(b) ¹ corresponds to afourth antenna port; in the third structure, V_(a) ⁰ corresponds to thefirst antenna port, and V_(a) ¹ corresponds to the fourth antenna port;in the fourth structure, V_(b) ⁰ corresponds to the second antenna port,and V_(b) ¹ corresponds to the third antenna port, where V_(a) ⁰ andV_(a) ¹ are elements in the vector V_(a), and V_(b) ⁰ and V_(b) ¹ areelements in the vector V_(b).

When the antenna ports are grouped into three groups, the first codebookset includes at least one of a first structure

$\begin{bmatrix}V_{a} \\0 \\0\end{bmatrix},$

a second structure

$\begin{bmatrix}0 \\V_{b} \\0\end{bmatrix},$

a third structure

$\begin{bmatrix}0 \\0 \\V_{c}\end{bmatrix},$

a fourth structure

$\begin{bmatrix}V_{a} \\0 \\V_{c}\end{bmatrix},$

a fifth structure

$\begin{bmatrix}V_{a} \\V_{b} \\0\end{bmatrix},$

or a sixth structure

$\begin{bmatrix}0 \\V_{b} \\V_{c}\end{bmatrix},$

Vectors V_(a), V_(b), and V_(c) each correspond to one group of antennaports.

In an embodiment of the present invention, the present inventionprovides a combination of the first structure and the second structurecorresponding to a value of the rank indicator.

Generally, an element in a non-zero vector included in the firstcodebook is in a form of a complex number. For a complex number α·e^(β),α is referred to as an amplitude part, and is a real number, and e^(β)is referred to as a phase part. In still another embodiment of thepresent invention, at least one first codebook meets a first condition.The present invention provides several definitions of the firstcondition that can be implemented. In the present invention, unlessotherwise limited, P, Q, and K are any positive integers.

First Definition of the First Condition:

A vector set formed by all first phase vectors and a discrete Fouriertransform matrix DFT matrix meet a first correspondence that the vectorset formed by the first phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the DFT matrix, wherean element in a P^(th) row and a Q^(th) column in the phase matrix ofthe DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the first phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding first phase vector, where P, Q, and K areany positive integers.

A general expression of the discrete Fourier transform matrix DFT matrixis:

$M_{dft} = {{\frac{1}{\sqrt{N}}\begin{bmatrix}1 & 1 & 1 & 1 & \ldots & 1 \\1 & \omega & \omega^{2} & \omega^{3} & \ldots & \omega^{N - 1} \\1 & \omega^{2} & \omega^{4} & \omega^{6} & \ldots & \omega^{2{({N - 1})}} \\1 & \omega^{3} & \omega^{6} & \omega^{9} & \ldots & \omega^{3{({N - 1})}} \\M & M & M & M & \; & M \\1 & \omega^{N - 1} & \omega^{2{({N - 1})}} & \omega^{3{({N - 1})}} & \ldots & \omega^{{({N - 1})}{({N - 1})}}\end{bmatrix}}.}$

The phase matrix of the DFT matrix is:

$M_{dft\_ phase} = {\begin{bmatrix}1 & 1 & 1 & 1 & \ldots & 1 \\1 & \omega & \omega^{2} & \omega^{3} & \ldots & \omega^{N - 1} \\1 & \omega^{2} & \omega^{4} & \omega^{6} & \ldots & \omega^{2{({N - 1})}} \\1 & \omega^{3} & \omega^{6} & \omega^{9} & \ldots & \omega^{3{({N - 1})}} \\M & M & M & M & \; & M \\1 & \omega^{N - 1} & \omega^{2{({N - 1})}} & \omega^{3{({N - 1})}} & \ldots & \omega^{{({N - 1})}{({N - 1})}}\end{bmatrix}.}$

A value of N is an order in a case in which the DFT matrix is a squarematrix. For example, in

$\quad{\begin{bmatrix}V_{a} \\0\end{bmatrix},}$

if Va is four-dimensional, the order of the phase matrix of the DFTmatrix is 4. In an embodiment, a value of ω may be

$\omega = e^{j\frac{2\pi}{N}}$

$M_{{dft}_{—}{phase}_{—}4} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & \omega & \omega^{2} & \omega^{3} \\1 & \omega^{2} & \omega^{4} & \omega^{6} \\1 & \omega^{3} & \omega^{6} & \omega^{9}\end{bmatrix}.}$

For example, when the value of ω is

$e^{j\frac{2\pi}{32}},$

a form of a fourth-order DFT matrix

$M_{{dft\_ phase}\_ 4{\_ e}^{j\frac{2\pi}{32}}}$

is:

$M_{{dft\_ phase}\_ 4{\_ e}^{j\frac{2\pi}{32}}} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & e^{j\frac{2\pi}{32}} & e^{2\; j\frac{2\pi}{32}} & e^{3\; j\frac{2\pi}{32}} \\1 & e^{2j\frac{2\pi}{32}} & e^{4j\frac{2\pi}{32}} & e^{6j\frac{2\pi}{32}} \\1 & e^{3j\frac{2\pi}{32}} & e^{6j\frac{2\pi}{32}} & e^{9j\frac{2\pi}{32}}\end{bmatrix}.}$

Correspondingly, the set of corresponding columns in the phase matrix ofthe DFT matrix is:

$\left\{ V_{m}^{\prime} \right\} = {\left\{ {\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\e^{j\frac{2\pi}{32}} \\e^{2j\frac{2\pi}{32}} \\e^{3j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{2j\frac{2\pi}{32}} \\e^{4j\frac{2\pi}{32}} \\e^{6j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{3j\frac{2\pi}{32}} \\e^{6j\frac{2\pi}{32}} \\e^{9j\frac{2\pi}{32}}\end{bmatrix}} \right\}.}$

It should be understood that, in the present invention, the phase matrixof the DFT matrix is not necessarily a square matrix. More columns orrows may be selected according to an order. For example, the matrix maybe:

$M_{{dft\_ phase}\_ 4{\_ e}^{j\frac{2\pi}{32}}}^{\prime} = {\begin{bmatrix}1 & 1 & 1 & 1 & 1 \\1 & e^{j\frac{2\pi}{32}} & e^{2\; j\frac{2\pi}{32}} & e^{3\; j\frac{2\pi}{32}} & e^{4\; j\frac{2\pi}{32}} \\1 & e^{2j\frac{2\pi}{32}} & e^{4j\frac{2\pi}{32}} & e^{6j\frac{2\pi}{32}} & e^{8\; j\frac{2\pi}{32}} \\1 & e^{3j\frac{2\pi}{32}} & e^{6j\frac{2\pi}{32}} & e^{9j\frac{2\pi}{32}} & e^{12\; j\frac{2\pi}{32}}\end{bmatrix}.}$

The set of corresponding columns in the phase matrix of the DFT matrixis:

$\left\{ V_{m}^{\prime} \right\} = {\left\{ {\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\e^{j\frac{2\pi}{32}} \\e^{2j\frac{2\pi}{32}} \\e^{3j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{2j\frac{2\pi}{32}} \\e^{4j\frac{2\pi}{32}} \\e^{6j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{3j\frac{2\pi}{32}} \\e^{6j\frac{2\pi}{32}} \\e^{9j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{4j\frac{2\pi}{32}} \\e^{8j\frac{2\pi}{32}} \\e^{12j\frac{2\pi}{32}}\end{bmatrix}} \right\}.}$

It should be understood that, a quantity of rows or a quantity ofcolumns selected from the DFT matrix is not limited in the presentinvention. It should be understood that, the quantity of rows should beat least the same as a value of V_(a), and the quantity of columnsshould be at least the same as a quantity of first vectors in acodebook.

Second Definition of the First Condition:

A vector set formed by all second phase vectors and at least one CMPcodebook in a CMP codebook set meet a second correspondence that thevector set formed by the second phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the CMP codebookmatrix, where an element in a P^(th) row and a Q^(th) column in thephase matrix of the CMP codebook matrix is a phase part of an element ina P^(th) row and a Q^(th) column in the CMP codebook matrix, V_(a) partsof all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the second phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding second phase vector, where P, Q, and K areany positive integers, and the CMP codebook refers to a codebook inwhich only one layer in layers corresponding to each port is a non-zeroelement.

In all CMP codebooks, CMP codebooks in which column vectors aretwo-dimensional are:

TABLE 1 Codebook Quantity of layers index v = 1 v = 2 0$\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ 1 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}$ — 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}$ — 3 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}$ — 4 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\0\end{bmatrix}$ — 5 $\frac{1}{\sqrt{2}}\begin{bmatrix}0 \\1\end{bmatrix}$ —

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 1 are:

TABLE 2 Codebook Quantity of layers index v = 1 0-7$\frac{1}{2}\begin{bmatrix}1 \\1 \\1 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\j \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\{- 1} \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\{- j} \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\1 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\j \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\{- 1} \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\{- j} \\{- 1}\end{bmatrix}$ 8-15 $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\1 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\j \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\{- 1} \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\{- j} \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\1 \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\j \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\{- 1} \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\{- j} \\1\end{bmatrix}$ 16-23 $\frac{1}{2}\begin{bmatrix}1 \\0 \\1 \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\{- 1} \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\j \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\{- j} \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\{- j}\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 2 are:

TABLE 3 Code- book Quantity of layers index v = 2 0-3$\frac{1}{2}\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}$ 4-7 $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}$ 8-11 $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & {- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & {- 1}\end{bmatrix}$ 12-15 $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 1 \\1 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & {- 1} \\1 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 1 \\{- 1} & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & {- 1} \\{- 1} & 0\end{bmatrix}$

For example, when the index in Table 3 is 0, the subset of the set ofcorresponding column vectors in the phase matrix of the correspondingCMP codebook matrix is:

$\left\{ {\begin{bmatrix}e^{0} \\e^{0} \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\e^{0} \\e^{{- j}\frac{\pi}{2}}\end{bmatrix}} \right\}.$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 3 are:

TABLE 4 Quantity of layers Codebook index v = 3 0-3$\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\{- 1} & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\{- 1} & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ 4-7 $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\{- 1} & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\{- 1} & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ 8-11 $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1 \\{- 1} & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0 \\{- 1} & 0 & 0\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 4 are:

TABLE 5 Codebook Quantity of layers index v = 4 0$\frac{1}{2}\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}$

Third Definition of the First Condition:

A vector set formed by all third phase vectors is a subset of a setformed by corresponding sub-vectors in a householder transform codebook,where a householder transform expression is W_(n)=I−u_(n)u_(n)^(H)/u_(n) ^(H)u_(n).

V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the third phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding third phase vector.

For example, the third phase vectors are a subset of a set formed byphase parts of W_(index) ^({α) ^(i) ^(}) in a matrix corresponding todifferent quantities of layers and different codebook indexes in Table6. The index corresponds to different codebook indexes. {α_(i)}corresponds to an integer set, and is used to indicate that differentcolumns in W_(index) ^({α) ^(i) ^(}) are selected as third phasevectors. In Table 6, U_(n) is a corresponding U_(n) in the householdertransform, and I is a unit matrix.

It should be understood that, in the present invention, the phase vectorof the V_(a) is not limited only to cases or relationships shown in thefirst definition of the first condition, the second definition of thefirst condition, and the third definition of the first condition. Thecodebook may further be a codebook defined for two antennas, fourantennas, or eight antennas in LTE.

TABLE 6 Codebook Number of layers ν index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1−1]^(T) W₀ ^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{squareroot over (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁^({12})/{square root over (2)} W₁ ^({123})/{square root over (3)} W₁^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over(2)} W₂ ^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1−j]^(T) W₃ ^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{squareroot over (3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)}−j (1 − j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square rootover (2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1− j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

In still another embodiment of the present invention, at least one firstcodebook meets a second condition. The present invention providesseveral definitions of the second condition that can be implemented.

First Definition of the Second Condition:

A vector set formed by all fourth phase vectors and a discrete Fouriertransform matrix DFT matrix meet a third correspondence that the vectorset formed by the fourth phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the DFT matrix, wherean element in a P^(th) row and a Q^(th) column in the phase matrix ofthe DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fourth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fourth phase vector.

Second Definition of the Second Condition:

A vector set formed by all fifth phase vectors and at least one CMPcodebook in a CMP codebook set meet a fourth correspondence that thevector set formed by the fifth phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the CMP codebookmatrix, where an element in a P^(th) row and a Q^(th) column in thephase matrix of the CMP is a phase part of an element in a P^(th) rowand a Q^(th) column in the CMP codebook matrix, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fifth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fifth phase vector, where P, Q, and K areany positive integers.

Third Definition of the Second Condition:

A vector set formed by all sixth phase vectors is a set formed bycorresponding sub-vectors in a householder transform codebook, whereV_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the sixth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding sixth phase vector.

It should be understood that, in the present invention, a value of theV_(b) is not limited only to cases or relationships shown in the firstdefinition of the second condition, the second definition of the secondcondition, and the third definition of the second condition. The presentinvention requests to protect correspondences according to the secondcondition: a relationship between the fourth phase vectors and differentDFT matrices formed by different parameters, a relationship between thefifth phase vectors and the CMP codebook set, and a relationship betweenthe sixth phase vectors and the householder codebook formed by differentoriginal vectors through householder transforms.

It should be understood that, due to independence, in one codebook, whenthe first codebook meets any definition of the first condition, a secondcodebook may meet any definition of the second condition. For example,in the first codebook, that the vector set formed by the first phasevectors is the subset of the set of corresponding column vectors in thephase matrix of the DFT matrix is met; in the second codebook, that thevector set formed by the fifth phase vectors is the subset of the set ofcorresponding column vectors in the phase matrix of the CMP codebookmatrix, or any combination thereof is met.

In still another embodiment of the present invention, at least one firstcodebook meets a third condition:

In all first amplitude vectors corresponding to {V_(m)}, at least onefirst amplitude vector is different from all second amplitude vectorscorresponding to the {V_(n)}; and/or in all second amplitude vectorscorresponding to the {V_(n)}, at least one second amplitude vector isdifferent from all first amplitude vectors corresponding to the {V_(m)}.V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form the set {V_(m)}, amplitude parts of allelements in each sub-vector of the {V_(m)} form the first amplitudevector, and a phase part of a K^(th) element in each sub-vector of the{V_(m)} is a K^(th) element of each corresponding first amplitudevector; and V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form the set {V_(n)}, amplitude parts of V_(b) allelements in each sub-vector of the {V_(n)} form the second amplitudevector, and an amplitude part of a K^(th) element in each sub-vector ofthe {V_(n)} is a K^(th) element of each corresponding second amplitudevector. In this embodiment, in a sub-vector included in each firstcodebook, an amplitude part of each element corresponds to power of anantenna port. In this embodiment, in a sub-vector included in each firstcodebook, amplitude vectors of each group of antenna ports aredetermined independently according to tilt characteristics of this groupof antenna ports (tilts may be classified into electrical tilts andmechanical tilts; an electrical tilt means that weighted vectors ofmultiple antenna elements corresponding to one antenna port make themultiple antenna elements form a beam pointing to a tilt). For example,all tilts of the first group of antenna ports are 12 degrees, and alltilts of the second group of antenna ports are 3 degrees; it is assumedthat a horizontal plane is 0 degrees and that those downward arepositive tilts. In this case, energies received from the two groups ofantenna ports by the first network device in a location are different.Therefore, independent control may be performed on amplitudes ofcodebooks of the two groups of antenna ports, so that receptionperformance is optimized.

Optionally, in step 101, the first codebook set is obtained before thefirst codebook is selected. In an embodiment of the present invention,the first codebook set may be pre-stored in the first network device, ordelivered to the first network device by the second network device oranother apparatus.

Optionally, at least one first configuration message is received, whereeach first configuration message is used to determine a sub-vector setof phase parts corresponding to one group of antenna ports, and aquantity of the at least one first configuration message is equal to aquantity of groups of the antenna ports; and/or at least one secondconfiguration message is received, where each second configurationmessage is used to determine a sub-vector set of amplitude partscorresponding to one group of antenna ports, and a quantity of the atleast one second configuration message is equal to a quantity of groupsof the antenna ports. In an embodiment, the first configuration messageis configured by the second network device by using higher layersignaling or dynamic signaling; and/or the second configuration messageis configured by the second network device by using higher layersignaling or dynamic signaling. In another embodiment, the firstconfiguration message is obtained by the first network device bymeasuring the reference signal; and/or the second configuration messageis obtained by the first network device by measuring the referencesignal.

In an embodiment, the present invention provides possible cases of acodebook set having the first structure and the second structure. Itshould be understood that, the first codebook that the present inventionrequests to protect may be but is not limited to the followingstructures:

1. the first codebook is one of the following matrices:

${\begin{bmatrix}{V_{a}(i)} \\0\end{bmatrix}\mspace{14mu} {{or}\mspace{14mu}\begin{bmatrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{bmatrix}}},$

where a value of a rank indicator is 1, a non-zero sub-vectorrepresented by V_(a)(x) is a sub-vector in the first vector set {V_(m)}and has a sequence number x, a non-zero sub-vector represented byV_(b)(y) is a sub-vector in the first vector set {V_(n)} and has asequence number y, 0<i≤N₁, and 0<i′≤N₁, where N₁ represents a quantityof sub-vectors in the {V_(m)}, and N₁′ represents a quantity ofsub-vectors in the {V_(n)}; or

2. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} \\0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 \\0 & {V_{b}(i)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},{{or}\mspace{14mu}\begin{bmatrix}0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}},$

where a value of a rank indicator is 2, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁, and0<j′≤N₁; or

3. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},{\quad{{\begin{bmatrix}0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}\mspace{14mu} {{or}\mspace{14mu}\begin{bmatrix}0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}},}}}}$

where a value of a rank indicator is 3, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, and 0<k′≤N₁; or

4. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack,{\quad\left\lbrack {\left. \quad\begin{matrix}0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack, {{or}{\quad\mspace{14mu} {\left\lbrack \begin{matrix}0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack ,}}}} \right.}}}}}}}}}}}}}}$

or where a value of a rank indicator is 4, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, and 0<l′≤N₁; or

5. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},{\quad{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\quad\left\lbrack {\left. \quad\begin{matrix}0 & 0 & 0 & {V_{a}(1)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(1)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack ,{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(4)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & 0 & 0 & {V_{a}(1)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},{{or}\mspace{14mu}\begin{bmatrix}0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}},}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} \right.}}}}}}}}}}}}}}}$

where a value of a rank indicator is 5, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, and 0<m′≤N₁; or

6. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & 0\end{bmatrix},{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack,}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(5)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack,}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(1)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack,}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}(j)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}(i)} & {V_{b}(j)} & 0 & {V_{b}(k)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}(k)}^{\prime} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack,}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack,}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack, {{or}{\quad\mspace{14mu} {\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix},}}}}}}}}}}}}}}}$

where a value of a rank indicator is 6, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁, and0<n′≤N₁; or

7. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack  {\quad\left\lbrack {\quad {\left. \quad\begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}}}}}}}}}}} \right.}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}(i)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(4)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{b}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad {\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{a}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack ,}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

where a value of a rank indicator is 7, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁,0<n′≤N₁, 0<p≤N₁, and 0<p′≤N₁; or

8. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} & {V_{a}(q)} \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}{\quad{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}(2)} & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack {{{\left. \quad\begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}(2)} & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack {\left. \quad\begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\quad \right.}\quad \right.}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\quad} {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix} {\quad\quad}{\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack  {\quad{\quad {\quad{\quad {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack  {\quad{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix} {\quad\quad}{\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad {\quad{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} {\quad\quad} {\quad\quad}}\quad}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {{V_{b}\left( l^{\prime} \right)}}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {{V_{b}\left( m^{\prime} \right)}}\end{matrix} \right\rbrack}\quad} {\quad{\quad {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{{{{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack {\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack {\quad {{{\quad\quad}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack} {\quad{\quad {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack {\quad\quad} {\quad {\quad{\quad {\quad{\quad{\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\quad{\quad{\quad{\quad{\quad{\quad{\quad{{\quad\quad} {\quad\quad}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad\quad} {\quad {\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\quad{\quad{\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack  {\quad{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}(i)} & 0 & {V_{b}(j)}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0 & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{{{{{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{A}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\quad{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\quad {\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad {\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack} {\quad{\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)} & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}{\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack  {\quad{\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)} & {V_{b}\left( q^{\prime} \right)}\end{matrix} \right\rbrack ,}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

where a value of a rank indicator is 8, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁,0<n′≤N₁, 0<p≤N₁, 0<p′≤N₁, 0<q≤N₁, and 0<q′≤N₁, where for parameters ofi, j, k, l, m, n, p, q, and the like, every two of the sub-vectorscorresponding to the V_(a) parts are unequal, and for parameters of i′,j′, k′, l′, m′, n′, p′, q′, and the like, every two of the sub-vectorscorresponding to the V_(b) parts are unequal.

It should be understood that, in the illustrated possible forms of thefirst codebook included in the first codebook set, i, j, k, l, m, n, p,and q are only for distinguishing different codebook vectors.

Further, in an embodiment of the present invention, V_(a) parts of allfirst sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(K)}, V_(b) parts of allsecond sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(L)}, and thecorresponding {V_(K)} and {V_(L)} in the same first codebook meet afourth condition, where the fourth condition is: phase parts of asub-vector V_(k) in the {V_(k)} form a vector V_(k)′, vectors V_(k)′corresponding to all sub-vectors V_(k) in the {V_(k)} form a set{V_(k)′}, phase parts of a sub-vector V_(L) in the {V_(L)} form a vectorV_(L)′, vectors V_(L)′ corresponding to all sub-vectors V_(L) in the{V_(L)} form a set {V_(L)′}, and {V_(k)′}≠{V_(L)′} holds true. Accordingto concepts of sets, when a quantity of dimensions of the {V_(k)′} and aquantity of dimensions of the {V_(L)′} are unequal, {V_(k)′}≠{V_(L)′}holds true; when a quantity of dimensions of the {V_(k)′} and a quantityof dimensions of the {V_(L)′} are equal, but a quantity of sub-vectorsincluded in the {V_(k)′} and a quantity of sub-vectors included in the{V_(L)′} are unequal, {V_(k)′}≠{V_(L)′} holds true; or when a quantityof dimensions of the {V_(k)′} and a quantity of dimensions of the{V_(L)′} are equal, and a quantity of sub-vectors included in the{V_(k)′} and a quantity of sub-vectors included in the {V_(L)′} areequal, but the sub-vectors included in the {V_(k)′} are different fromthe sub-vectors included in the {V_(L)′}, {V_(k)′}≠{V_(L)′} also holdstrue.

In another embodiment of the present invention, when the value of the RIis greater than 1, V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(M)}, V_(b) parts of allsecond sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(N)}, and thecorresponding {V_(M)} and {V_(N)} in the same first codebook meet afifth condition, where the fifth condition is: amplitude parts of asub-vector V_(M) in the {V_(M)} form a vector V_(M)′, vectors V_(M)′corresponding to all sub-vectors V_(M) in the {V_(M)} form a set{V_(M)′}, amplitude parts of a sub-vector V_(N) in the {V_(N)} form avector V_(N)′, vectors V_(N)′ corresponding to all sub-vectors V_(N) inthe {V_(N)} form a set {V_(N)′}, and {V_(M)′}≠{V_(N)′} holds true.

According to concepts of sets, when a quantity of dimensions of the{V_(M)′} and a quantity of dimensions of the {V_(N)′} are unequal,{V_(M)′}≠{V_(N)′} holds true; when a quantity of dimensions of the{V_(M)′} and a quantity of dimensions of the {V_(N)′} are equal, but aquantity of sub-vectors included in the {V_(M)′} and a quantity ofsub-vectors included in the {V_(N)′} are unequal, {V_(M)′}≠{V_(N)′}holds true; or when a quantity of dimensions of the {V_(M)′} and aquantity of dimensions of the {V_(N)′} are equal, and a quantity ofsub-vectors included in the {V_(M)′} and a quantity of sub-vectorsincluded in the {V_(N)′} are equal, but the sub-vectors included in the{V_(M)′} are different from the sub-vectors included in the {V_(N)′},{V_(M)′}≠{V_(N)′} also holds true.

In the foregoing embodiment, with the first codebook that makes the{V_(k)′}≠{V_(L)′} and/or {V_(M)′}≠{V_(N)′} relation hold true, flexibleconfigurations of the first structure and the second structure areimplemented, and a codebook is better matched with a channel.

The following provides relationships of amplitude vectors respectivelycorresponding to

$\begin{bmatrix}V_{a} \\0\end{bmatrix}{\quad\mspace{14mu} {{{and}\mspace{14mu}\begin{bmatrix}0 \\V_{b}\end{bmatrix}}{\quad.}}}$

A first relationship of amplitude vectors, a second relationship ofamplitude vectors, and a third relationship of amplitude vectors eachprovide a configuration mode of a relationship between elements includedin each sub-vector. The third relationship of amplitude vectors and afourth relationship of amplitude vectors provide relationships betweendifferent codebook vectors in a codebook. The second network device mayconfigure different amplitude vectors according to channel conditions,so that transmission efficiency is higher. The definitions of amplitudevectors are already described, and are not further described herein.

For example, a codebook M₂ in a codebook set is:

$\begin{bmatrix}{a_{1}e^{j\; w_{1}}} & 0 & {b_{1}e^{j\; \theta_{1}}} & {c_{1}e^{j\; \gamma_{1}}} & 0 \\{a_{2}e^{j\; w_{2}}} & 0 & {b_{2}e^{j\; \theta_{2}}} & {c_{2}e^{j\; \gamma_{2}}} & 0 \\{a_{3}e^{j\; w_{3}}} & 0 & {b_{3}e^{j\; \theta_{3}}} & {c_{3}e^{j\; \gamma_{3}}} & 0 \\{a_{4}e^{j\; w_{4}}} & 0 & {b_{4}e^{j\; \theta_{4}}} & {c_{4}e^{j\; \gamma_{4}}} & 0 \\0 & {d_{1}e^{j\; \alpha_{1}}} & 0 & 0 & {g_{1}e^{j\; \beta_{1}}} \\0 & {d_{2}e^{j\; \alpha_{2}}} & 0 & 0 & {g_{2}e^{j\; \beta_{2}}}\end{bmatrix}.$

If M₂ meets the first relationship of amplitude vectors: at least twoelements in an amplitude vector in V_(a) of each first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are unequal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are unequal, at least two values in a₁, a₂, a₃,and a₄ are unequal; at least two values in b₁, b₂, b₃, and b₄ areunequal; at least two values in c₁, c₂, c₃, and c₄ are unequal; d₁≠d₂;and g₁≠g₂.

If M₂ meets the second relationship of amplitude vectors: at least twoelements in an amplitude vector in V_(a) of each first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are unequal, and all elements in an amplitudevector in V_(b) of each second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are equal, at least two values in a₁, a₂, a₃, anda₄ are unequal; at least two values in b₁, b₂, b₃, and b₄ are unequal;at least two values in c₁, c₂, c₃, and c₄ are unequal; d₁≠d₂; and g₁=g₄.

If M₂ meets the third relationship of amplitude vectors: all elements inan amplitude vector in V_(a) of each first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are equal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are unequal, a₁=a₂=a₃=a₄; b₁=b₂=b₃=b₄;c₁=c₂=c₃=c₄; d₁≠d₂; and g₁≠g₂.

If M₂ meets the fourth relationship of amplitude vectors: at least twoamplitude vectors in a vector set formed by amplitude vectors in V_(a)of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are different, amplitude vectors in V_(a) of allcorresponding first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in M₂ are

$\begin{bmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4}\end{bmatrix},\begin{bmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4}\end{bmatrix},{{and}\mspace{14mu}\begin{bmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4}\end{bmatrix}},$

where at least two vectors of

$\begin{bmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4}\end{bmatrix},\begin{bmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4}\end{bmatrix},{{and}\mspace{14mu}\begin{bmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4}\end{bmatrix}}$

are different.

A fifth relationship of amplitude vectors is: at least two amplitudevectors in a vector set formed by amplitude vectors in V_(b) of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are different.

In this case, amplitude vectors in V_(b) of all corresponding secondsub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in M₂ are

$\quad{{\begin{bmatrix}d_{1} \\d_{2}\end{bmatrix}\mspace{14mu} {{and}\mspace{14mu}\begin{bmatrix}g_{1} \\g_{2}\end{bmatrix}}},{{{where}\mspace{14mu}\begin{bmatrix}d_{1} \\d_{2}\end{bmatrix}}\mspace{14mu} {{and}\mspace{14mu}\begin{bmatrix}g_{1} \\g_{2}\end{bmatrix}}}}$

are unequal.

In the present invention, the amplitude vector in the V_(a) refers to avector formed by the amplitude parts of the V_(a), and the amplitudevector in the V_(b) refers to a vector formed by the amplitude parts ofthe V_(b). For example,

if the V_(a) part is

$\begin{bmatrix}\frac{1}{\sqrt{20}} \\{\frac{2}{\sqrt{20}}e^{4j\frac{2\pi}{32}}} \\{\frac{3}{\sqrt{20}}e^{8j\frac{2\pi}{32}}} \\{\frac{4}{\sqrt{20}}e^{12j\frac{2\pi}{32}}}\end{bmatrix},$

the amplitude vector in the V_(a) is:

$\begin{bmatrix}\frac{1}{\sqrt{20}} \\\frac{2}{\sqrt{20}} \\\frac{3}{\sqrt{20}} \\\frac{4}{\sqrt{20}}\end{bmatrix};$

if the V_(a) part is

$\begin{bmatrix}\frac{1}{\sqrt{20}} \\{\frac{2}{\sqrt{20}}e^{4j\frac{2\pi}{32}}} \\{\frac{3}{\sqrt{20}}e^{8j\frac{2\pi}{32}}} \\{\frac{4}{\sqrt{20}}e^{12j\frac{2\pi}{32}}}\end{bmatrix},$

the amplitude vector in the V_(b) is:

$\begin{bmatrix}\frac{1}{\sqrt{20}} \\\frac{2}{\sqrt{20}} \\\frac{3}{\sqrt{20}} \\\frac{4}{\sqrt{20}}\end{bmatrix}.$

FIG. 7 shows a flowchart of a method embodiment according to the presentinvention, which is specifically as follows:

Step 201: Send a reference signal to a first network device, where thereference signal is used by the first network device to perform ameasurement to obtain a measurement result.

Step 202: Receive a codebook index sent by the first network device,where the codebook index corresponds to a first codebook determined inthe first codebook set by the first network device, and the codebookindex is determined by the first network device according to themeasurement result.

Step 203: Determine, according to the codebook index, the first codebookdetermined in the first codebook set by the first network device.

The first codebook set includes at least two first codebooks. Asub-vector W_(x) of each first codebook is formed by a zero vector and anon-zero vector, and the vectors forming the W_(x) correspond todifferent groups of antenna ports; in each first codebook, differentsub-vectors W_(x) are formed according to a same structure or differentstructures; formation according to the same structure is: for differentsub-vectors W_(x)(1) and W_(x)(2), a location of a non-zero vector inthe W_(x)(1) is the same as a location of a non-zero vector in theW_(x)(2); and formation according to different structures is: fordifferent sub-vectors W_(x)(1) and W_(x)(2), a location of a non-zerovector in the W_(x)(1) is different from a location of a non-zero vectorin the W_(x)(2).

It should be understood that, in the present invention, a zero vectormay be a zero element with a length of 1, and a non-zero vector may be anon-zero element with a length of 1. Generally, for a passive antenna, adowntilt in a vertical direction is fixed. Therefore, for multiplespatially multiplexed data streams, adjustments can be made to multiplehorizontal beams only in a plane with a fixed downtilt in the verticaldirection, and the multiple data streams cannot be multiplexed morefreely in planes with multiple downtilts. In addition, if antenna portsare grouped according to different downtilts, a codebook structureprovided by the present invention may be configured independentlyaccording to transmit power of different groups of antenna ports, sothat flexibility and MIMO performance are improved.

In an embodiment of the present invention, when antenna ports aregrouped according to tilts in the vertical direction, parameters ofcodebook vectors in a codebook may be configured independently accordingto different tilts, so that an objective of flexibly adapting to datatransmission efficiency is achieved. In this embodiment, two tilts inthe vertical direction are used as an example (this method is alsoapplicable to more than two tilts). In each column in the firstcodebook, one group of antenna ports corresponds to a non-zero vector,and another group of antenna ports corresponds to a zero vector; or onegroup of antenna ports corresponds to a zero vector, and another groupof antenna ports corresponds to a non-zero vector, where the non-zerovector refers to a vector in which at least one element is a non-zeroelement, and the zero vector refers to a vector in which all elementsare zero elements. In the present invention, when first n1 elements in avector included in a codebook correspond to one group of antenna ports,and last n2 elements correspond to another group of antenna ports, astructure of this vector is

$\begin{bmatrix}V_{1} \\V_{2}\end{bmatrix},$

where V₁ is n1-dimensional, and V₂ is n2-dimensional. In this case, eachfirst codebook includes at least one first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

having a first structure and/or at least one second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

having a second structure; where V_(a) in

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

is an n1-dimensional non-zero vector and corresponds to a first group ofantenna ports; 0 in

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

represents an n2-dimensional zero vector and corresponds to a secondgroup of antenna ports; V_(b) in

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

is an n2-dimensional non-zero vector and corresponds to the second groupof antenna ports; and 0 in

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

represents an n1-dimensional zero vector and corresponds to the firstgroup of antenna ports. It should be understood that, the presentinvention is not limited to the case of grouping into only two groups.In an actual application, antenna ports are grouped into more groupsaccording to other factors such as different downtilts or signal qualityor the like. In a specific measurement process, codebooks in the firstcodebook set are traversed, so that a first codebook that best matches atransmission characteristic is determined and used for channeltransmission.

It should be understood that, the structure of the sub-vector in thefirst codebook may be but is not limited to the foregoing firststructure or the second structure. Optionally, locations of sub-vectorsof the zero vector and the non-zero vector in the first codebook may bedifferent. In an embodiment of the present invention, in a case of fourantenna ports, elements in vectors in the first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

having the first structure are represented as

$\begin{bmatrix}V_{a}^{0} \\V_{a}^{1} \\0 \\0\end{bmatrix},$

and elements in vectors in the second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

having the second structure are represented as

$\begin{bmatrix}0 \\0 \\V_{b}^{0} \\V_{b}^{1}\end{bmatrix},$

where V_(a) ⁰ and V_(a) ¹ are elements in the vector V_(a), and V_(b) ⁰and V_(b) ¹ are elements in the vector V_(b). In another embodiment ofthe present invention, when the antenna ports are grouped into twogroups, the first structure may be

$\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix},$

and the second structure may be

$\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix}.$

Likewise, when the antenna groups are grouped into two groups, inanother embodiment of the present invention, the first structure may be

$\begin{bmatrix}V_{a}^{0} \\0 \\0 \\V_{a}^{1}\end{bmatrix},$

and the second structure may be

$\begin{bmatrix}0 \\V_{b}^{0} \\V_{b}^{1} \\0\end{bmatrix}.$

Alternatively, the first codebook set includes at least one of thefollowing four structures: a first structure

$\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix},$

a second structure

$\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix},$

a third structure

$\begin{bmatrix}V_{a}^{0} \\0 \\0 \\V_{a}^{1}\end{bmatrix},$

or a fourth structure

$\begin{bmatrix}0 \\V_{b}^{0} \\V_{b}^{1} \\0\end{bmatrix}.$

V_(a) ⁰ and V_(a) ¹ are elements in the vector V_(a), and Va correspondsto one group of antenna ports. A correspondence is as follows: In thefirst structure, V_(a) ⁰ corresponds to a first antenna port, and V_(a)¹ corresponds to a third antenna port; in the second structure, V_(b) ⁰corresponds to a second antenna port, and V_(b) ¹ corresponds to afourth antenna port; in the third structure, V_(a) ⁰ corresponds to thefirst antenna port, and V_(a) ¹ corresponds to the fourth antenna port;in the fourth structure, V_(b) ⁰ corresponds to the second antenna port,and V_(b) ¹ corresponds to the third antenna port, where V_(a) ⁰ andV_(a) ¹ are elements in the vector V_(a), and V_(b) ⁰ and V_(b) ¹ areelements in the vector V_(b).

When the antenna ports are grouped into three groups, the first codebookset includes at least one of a first structure

$\begin{bmatrix}V_{a} \\0 \\0\end{bmatrix},$

a second structure

$\begin{bmatrix}0 \\V_{b} \\0\end{bmatrix},$

a third structure

$\begin{bmatrix}0 \\0 \\V_{c}\end{bmatrix},$

fourth structure

$\begin{bmatrix}V_{a} \\0 \\V_{c}\end{bmatrix},$

a fifth structure

$\begin{bmatrix}V_{a} \\V_{b} \\0\end{bmatrix},$

or a sixth structure

$\begin{bmatrix}0 \\V_{b} \\V_{c}\end{bmatrix}.$

Vectors V_(a), V_(b), and V_(c) each correspond to one group of antennaports.

In an embodiment of the present invention, the present inventionprovides a combination of the first structure and the second structurecorresponding to a value of the rank indicator.

Generally, an element in a non-zero vector included in the firstcodebook is in a form of a complex number. For a complex number α·e^(β),α is referred to as an amplitude part, and is a real number, and e^(β)is referred to as a phase part. In still another embodiment of thepresent invention, at least one first codebook meets a first condition.The present invention provides several definitions of the firstcondition that can be implemented. In the present invention, unlessotherwise limited, P, Q, and K are any positive integers.

First Definition of the First Condition:

A vector set formed by all first phase vectors and a discrete Fouriertransform matrix DFT matrix meet a first correspondence that the vectorset formed by the first phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the DFT matrix, wherean element in a P^(th) row and a Q^(th) column in the phase matrix ofthe DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the first phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding first phase vector, where P, Q, and K areany positive integers.

A general expression of the discrete Fourier transform matrix DFT matrixis:

$M_{dft} = {{\frac{1}{\sqrt{N}}\begin{bmatrix}1 & 1 & 1 & 1 & \ldots & 1 \\1 & \omega & \omega^{2} & \omega^{3} & \ldots & \omega^{N - 1} \\1 & \omega^{2} & \omega^{4} & \omega^{6} & \ldots & \omega^{2{({N - 1})}} \\1 & \omega^{3} & \omega^{6} & \omega^{9} & \ldots & \omega^{3{({N - 1})}} \\M & M & M & M & \; & M \\1 & \omega^{N - 1} & \omega^{2{({N - 1})}} & \omega^{3{({N - 1})}} & \ldots & \omega^{{({N - 1})}{({N - 1})}}\end{bmatrix}}.}$

The phase matrix of the DFT matrix is:

$M_{dft\_ phase} = {\begin{bmatrix}1 & 1 & 1 & 1 & \ldots & 1 \\1 & \omega & \omega^{2} & \omega^{3} & \ldots & \omega^{N - 1} \\1 & \omega^{2} & \omega^{4} & \omega^{6} & \ldots & \omega^{2{({N - 1})}} \\1 & \omega^{3} & \omega^{6} & \omega^{9} & \ldots & \omega^{3{({N - 1})}} \\M & M & M & M & \; & M \\1 & \omega^{N - 1} & \omega^{2{({N - 1})}} & \omega^{3{({N - 1})}} & \ldots & \omega^{{({N - 1})}{({N - 1})}}\end{bmatrix}.}$

A value of N is an order in a case in which the DFT matrix is a squarematrix. For example, in

$\begin{bmatrix}V_{a} \\0\end{bmatrix}{\quad,}$

if Va is four-dimensional, the order of the phase matrix of the DFTmatrix is 4. In an embodiment, a value of ω may be

$\omega = e^{j\frac{2\pi}{N}}$

$M_{{dft\_ phase}\_ 4} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & \omega & \omega^{2} & \omega^{3} \\1 & \omega^{2} & \omega^{4} & \omega^{6} \\1 & \omega^{3} & \omega^{6} & \omega^{9}\end{bmatrix}.}$

For example, when the value of ω is

$e^{j\frac{2\; \pi}{32}},$

a form of a fourth-order DFT matrix

$M_{{dft\_ phase}\_ 4{\_ e}^{j\frac{2\; \pi}{32}}}$

is:

$M_{{dft\_ phase}\_ 4{\_ e}^{j\frac{2\; \pi}{32}}} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & e^{j\frac{2\; \pi}{32}} & e^{2j\frac{2\; \pi}{32}} & e^{3j\frac{2\; \pi}{32}} \\1 & e^{2j\frac{2\; \pi}{32}} & e^{4j\frac{2\; \pi}{32}} & e^{6j\frac{2\; \pi}{32}} \\1 & e^{3j\frac{2\; \pi}{32}} & e^{6j\frac{2\; \pi}{32}} & e^{9j\frac{2\; \pi}{32}}\end{bmatrix}.}$

Correspondingly, the set of corresponding columns in the phase matrix ofthe DFT matrix is:

$\left\{ V_{m}^{\prime} \right\} = {\left\{ {\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\e^{j\frac{2\; \pi}{32}} \\e^{2j\frac{2\; \pi}{32}} \\e^{3j\frac{2\; \pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{2j\frac{2\; \pi}{32}} \\e^{4j\frac{2\; \pi}{32}} \\e^{6j\frac{2\; \pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{3j\frac{2\; \pi}{32}} \\e^{6j\frac{2\; \pi}{32}} \\e^{9j\frac{2\; \pi}{32}}\end{bmatrix}} \right\}.}$

It should be understood that, in the present invention, the phase matrixof the DFT matrix is not necessarily a square matrix. More columns orrows may be selected according to an order. For example, the matrix maybe:

$M_{{dft\_ phase}\_ 4{\_ e}^{j\frac{2\; \pi}{32}}}^{\prime} = {\begin{bmatrix}1 & 1 & 1 & 1 & 1 \\1 & e^{j\frac{2\; \pi}{32}} & e^{2j\frac{2\; \pi}{32}} & e^{3j\frac{2\; \pi}{32}} & e^{4j\frac{2\; \pi}{32}} \\1 & e^{2j\frac{2\; \pi}{32}} & e^{4j\frac{2\; \pi}{32}} & e^{6j\frac{2\; \pi}{32}} & e^{8j\frac{2\; \pi}{32}} \\1 & e^{3j\frac{2\; \pi}{32}} & e^{6j\frac{2\; \pi}{32}} & e^{9j\frac{2\; \pi}{32}} & e^{12j\frac{2\; \pi}{32}}\end{bmatrix}.}$

The set of corresponding columns in the phase matrix of the DFT matrixis:

$\left\{ V_{m}^{\prime} \right\} = {\left\{ {\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\e^{j\frac{2\; \pi}{32}} \\e^{2j\frac{2\; \pi}{32}} \\e^{3j\frac{2\; \pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{2j\frac{2\; \pi}{32}} \\e^{4j\frac{2\; \pi}{32}} \\e^{6j\frac{2\; \pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{3j\frac{2\; \pi}{32}} \\e^{6j\frac{2\; \pi}{32}} \\e^{9j\frac{2\; \pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{4j\frac{2\; \pi}{32}} \\e^{8j\frac{2\; \pi}{32}} \\e^{12j\frac{2\; \pi}{32}}\end{bmatrix}} \right\}.}$

It should be understood that, a quantity of rows or a quantity ofcolumns selected from the DFT matrix is not limited in the presentinvention. It should be understood that, the quantity of rows should beat least the same as a value of V_(a), and the quantity of columnsshould be at least the same as a quantity of first vectors in acodebook.

Second Definition of the First Condition:

A vector set formed by all second phase vectors and at least one CMPcodebook in a CMP codebook set meet a second correspondence that thevector set formed by the second phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the CMP codebookmatrix, where an element in a P^(th) row and a Q^(th) column in thephase matrix of the CMP codebook matrix is a phase part of an element ina P^(th) row and a Q^(th) column in the CMP codebook matrix, V_(a) partsof all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the second phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding second phase vector, where P, Q, and K areany positive integers, and the CMP codebook refers to a codebook inwhich only one layer in layers corresponding to each port is a non-zeroelement.

In all CMP codebooks, CMP codebooks in which column vectors aretwo-dimensional are:

TABLE 1 Codebook Quantity of layers index v = 1 v = 2 0$\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ 1 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}$ — 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}$ — 3 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}$ — 4 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\0\end{bmatrix}$ — 5 $\frac{1}{\sqrt{2}}\begin{bmatrix}0 \\1\end{bmatrix}$ —

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 1 are:

TABLE 2 Codebook Quantity of layers index v = 1 0-7$\frac{1}{2}\begin{bmatrix}1 \\1 \\1 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\j \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\{- 1} \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\{- j} \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\1 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\j \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\{- 1} \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\{- j} \\{- 1}\end{bmatrix}$ 8-15 $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\1 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\j \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\{- 1} \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\{- j} \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\1 \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\j \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\{- 1} \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\{- j} \\1\end{bmatrix}$ 16-23 $\frac{1}{2}\begin{bmatrix}1 \\0 \\1 \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\{- 1} \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\j \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\{- j} \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\{- j}\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 2 are:

TABLE 3 Codebook Quantity of layers index v = 2 0-3$\frac{1}{2}\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}$ 4-7 $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}$ 8-11 $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & {- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & {- 1}\end{bmatrix}$ 12-15 $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 1 \\1 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & {- 1} \\1 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 1 \\{- 1} & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & {- 1} \\{- 1} & 0\end{bmatrix}$

For example, when the index in Table 3 is 0, the subset of the set ofcorresponding column vectors in the phase matrix of the correspondingCMP codebook matrix is:

$\left\{ {\begin{bmatrix}e^{0} \\e^{0} \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\e^{0} \\e^{{- j}\; \frac{\pi}{2}}\end{bmatrix}} \right\}.$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 3 are:

TABLE 4 Quantity of layers Codebook index v = 3 0-3$\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\{- 1} & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\{- 1} & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ 4-7 $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\{- 1} & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\{- 1} & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ 8-11 $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1 \\{- 1} & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0 \\{- 1} & 0 & 0\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 4 are:

TABLE 5 Codebook Quantity of layers index v = 4 0$\frac{1}{2}\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}$

Third Definition of the First Condition:

A vector set formed by all third phase vectors is a subset of a setformed by corresponding sub-vectors in a householder transform codebook,where a householder transform expression is W_(n)=I−u_(n)u_(n)^(H)/u_(n) ^(H)u_(n).

V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the third phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding third phase vector.

For example, the third phase vectors are a subset of a set formed byphase parts of W_(index) ^({α) ^(i) ^(}) in a matrix corresponding todifferent quantities of layers and different codebook indexes in Table6. The index corresponds to different codebook indexes. {α_(i)}corresponds to an integer set, and is used to indicate that differentcolumns in W_(index) ^({α) ^(i) ^(}) are selected as third phasevectors. In Table 6, U_(n) is a corresponding U_(n) in the householdertransform, and I is a unit matrix.

It should be understood that, in the present invention, a value of theV_(a) is not limited only to cases or relationships shown in the firstdefinition of the first condition, the second definition of the firstcondition, and the third definition of the first condition. The codebookmay further be a codebook defined for two antennas, four antennas, oreight antennas in LTE.

TABLE 6 Codebook Number of layers ν index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1−1]^(T) W₀ ^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{squareroot over (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁^({12})/{square root over (2)} W₁ ^({123})/{square root over (3)} W₁^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over(2)} W₂ ^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1−j]^(T) W₃ ^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{squareroot over (3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)}−j (1 − j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square rootover (2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1− j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

In still another embodiment of the present invention, at least one firstcodebook meets a second condition. The present invention providesseveral definitions of the second condition that can be implemented.

First Definition of the Second Condition:

A vector set formed by all fourth phase vectors and a discrete Fouriertransform matrix DFT matrix meet a third correspondence that the vectorset formed by the fourth phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the DFT matrix, wherean element in a P^(th) row and a Q^(th) column in the phase matrix ofthe DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fourth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fourth phase vector.

Second Definition of the Second Condition:

A vector set formed by all fifth phase vectors and at least one CMPcodebook in a CMP codebook set meet a fourth correspondence that thevector set formed by the fifth phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the CMP codebookmatrix, where an element in a P^(th) row and a Q^(th) column in thephase matrix of the CMP is a phase part of an element in a P^(th) rowand a Q^(th) column in the CMP codebook matrix, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all V_(b)elements in each sub-vector of the {V_(n)} form the fifth phase vector,and a phase part of a K^(th) element in each sub-vector of the {V_(n)}is a K^(th) element of each corresponding fifth phase vector, where P,Q, and K are any positive integers.

Third Definition of the Second Condition:

A vector set formed by all sixth phase vectors is a set formed bycorresponding sub-vectors in a householder transform codebook, whereV_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the sixth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding sixth phase vector.

It should be understood that, in the present invention, a value of theV_(b) is not limited only to cases or relationships shown in the firstdefinition of the second condition, the second definition of the secondcondition, and the third definition of the second condition. The presentinvention requests to protect correspondences according to the secondcondition: a relationship between the fourth phase vectors and differentDFT matrices formed by different parameters, a relationship between thefifth phase vectors and the CMP codebook set, and a relationship betweenthe sixth phase vectors and the householder codebook formed by differentoriginal vectors through householder transforms.

It should be understood that, due to independence, in one codebook, whenthe first codebook meets any definition of the first condition, a secondcodebook may meet any definition of the second condition. For example,in the first codebook, that the vector set formed by the first phasevectors is the subset of the set of corresponding column vectors in thephase matrix of the DFT matrix is met; in the second codebook, that thevector set formed by the fifth phase vectors is the subset of the set ofcorresponding column vectors in the phase matrix of the CMP codebookmatrix, or any combination thereof is met.

In still another embodiment of the present invention, at least one firstcodebook meets a third condition:

In all first amplitude vectors corresponding to {V_(m)}, at least onefirst amplitude vector is different from all second amplitude vectorscorresponding to the {V_(n)}; and/or in all second amplitude vectorscorresponding to the {V_(n)}, at least one second amplitude vector isdifferent from all first amplitude vectors corresponding to the {V_(m)}.V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form the set {V_(m)}, amplitude parts of allelements in each sub-vector of the {V_(m)} form the first amplitudevector, and a phase part of a K^(th) element in each sub-vector of the{V_(m)} is a K^(th) element of each corresponding first amplitudevector; and V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form the set {V_(n)}, amplitude parts of allelements in each sub-vector of the {V_(n)} form the second amplitudevector, and an amplitude part of a K^(th) element in each sub-vector ofthe {V_(n)} is a K^(th) element of each corresponding second amplitudevector. In this embodiment, in a sub-vector included in each firstcodebook, an amplitude part of each element corresponds to power of anantenna port. In this embodiment, in a sub-vector included in each firstcodebook, amplitude vectors of each group of antenna ports aredetermined independently according to tilt characteristics of this groupof antenna ports (tilts may be classified into electrical tilts andmechanical tilts; an electrical tilt means that weighted vectors ofmultiple antenna elements corresponding to one antenna port make themultiple antenna elements form a beam pointing to a tilt). For example,all tilts of the first group of antenna ports are 12 degrees, and alltilts of the second group of antenna ports are 3 degrees; it is assumedthat a horizontal plane is 0 degrees and that those downward arepositive tilts. In this case, energies received from the two groups ofantenna ports by the first network device in a location are different.Therefore, independent control may be performed on amplitudes ofcodebooks of the two groups of antenna ports, so that receptionperformance is optimized.

Optionally, in step 202, the first codebook set is obtained before thefirst codebook is selected. In an embodiment of the present invention,the first codebook set may be pre-stored in the first network device, ordelivered to the first network device by a second network device oranother apparatus.

Optionally, at least one first configuration message is sent to thefirst network device, where each first configuration message is used todetermine a sub-vector set of phase parts corresponding to one group ofantenna ports, and a quantity of the at least one first configurationmessage is equal to a quantity of groups of the antenna ports; and/or atleast one second configuration message is sent to the first networkdevice, where each second configuration message is used to determine asub-vector set of amplitude parts corresponding to one group of antennaports, and a quantity of the at least one second configuration messageis equal to a quantity of groups of the antenna ports. The referencesignal is further used to indicate the first configuration message;and/or the reference signal is further used to indicate the secondconfiguration message, so that the first network device acquires thefirst configuration message and or the second configuration messageaccording to the reference signal.

In an embodiment, the first configuration message is configured by thesecond network device by using higher layer signaling or dynamicsignaling; and/or the second configuration message is configured by thesecond network device by using higher layer signaling or dynamicsignaling.

In an embodiment, the present invention provides possible cases of acodebook set having the first structure and the second structure. Itshould be understood that, the first codebook that the present inventionrequests to protect may be but is not limited to the followingstructures:

1. the first codebook is one of the following matrices:

$\quad{\begin{bmatrix}{V_{a}(i)} \\0\end{bmatrix}\mspace{14mu} {or}\mspace{14mu} {\quad{\begin{bmatrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{bmatrix},}}}$

where a value of a rank indicator is 1, a non-zero sub-vectorrepresented by V_(a)(x) is a sub-vector in the first vector set {V_(m)}and has a sequence number x, a non-zero sub-vector represented byV_(b)(y) is a sub-vector in the first vector set {V_(n)} and has asequence number y, 0<i≤N₁, and 0<i′≤N₁, where N₁ represents a quantityof sub-vectors in the {V_(m)}, and N₁′ represents a quantity ofsub-vectors in the {V_(n)}; or

2. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} \\0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},{{or}\mspace{14mu}\begin{bmatrix}0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}},$

where a value of a rank indicator is 2, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁, and0<j′≤N₁; or

3. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{b}(j)} \\{V_{a}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},{{or}\mspace{14mu}\begin{bmatrix}0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}},$

where a value of a rank indicator is 3, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, and 0<k′≤N₁; or

4. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\0 & 0 & 0\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 \\0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} \\0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & 0 & 0 \\0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & {V_{a}(i)} & 0 \\{V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & 0 & {V_{a}(i)} \\{V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix}} \right\rbrack,{{or}\mspace{14mu}\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & 0 & 0 \\{V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix}} \right\rbrack},$

where a value of a rank indicator is 4, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, and 0<l′≤N₁; or

5. the first codebook is one of the following matrices:

$\begin{matrix}{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & 0 & 0\end{bmatrix},} & \mspace{11mu} \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & 0 & 0\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & 0 & {V_{a}(1)} & {V_{a}(j)} \\{V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & 0 & 0 & {V_{a}(1)} \\{V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix}} \right\rbrack,} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(4)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},} & \; \\{\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}{V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}{V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}{V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}{V_{a}(i)} \\0\end{matrix}\begin{matrix}0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}{V_{a}(i)} & 0 & 0 & 0 \\0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix}} \right\rbrack,\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix}} \right\rbrack,} & \; \\{\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & 0 & {V_{a}(1)} & 0 \\{V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix}} \right\rbrack,{{or}\left\lbrack {\begin{matrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{matrix}\begin{matrix}0 & 0 & 0 & 0 \\{V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix}} \right\rbrack},} & \;\end{matrix}$

where a value of a rank indicator is 5, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, and 0<m′≤N₁; or

6. the first codebook is one of the following matrices:

$\begin{matrix}{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(5)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & 0 & {V_{a}(1)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & 0 & {V_{a}(1)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}(j)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}(i)} & {V_{b}(j)} & 0 & {V_{b}(k)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},} & \; \\{\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},{{or}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}},} & \;\end{matrix}$

where a value of a rank indicator is 6, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁, and0<n′≤N₁; or

7. the first codebook is one of the following matrices:

$\begin{matrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(l)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(4)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(n)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix} & \; \\\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix} & \; \\{\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix},} & \;\end{matrix}$

where a value of a rank indicator is 7, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁,0<n′≤N₁, 0<p≤N₁, and 0<p′≤N₁; or

8. the first codebook is one of the following matrices:

$\quad{{{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} & {V_{a}(q)} \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}(2)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}(2)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}(i)} & 0 & {V_{b}(j)}\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0 & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)} & 0\end{bmatrix}$

${{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}$

${{{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)} & {V_{b}\left( q^{\prime} \right)}\end{bmatrix}},$

where a value of a rank indicator is 8, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, and 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁,0<n′≤N₁, 0<p≤N₁, 0<p′≤N₁, 0<q≤N₁, and 0<q′≤N₁, where for parameters ofi, j, k, l, m, n, p, q, and the like, every two of the sub-vectorscorresponding to the V_(a) parts are unequal, and for parameters of i′,j′, k′, l′, m′, n′, p′, q′, and the like, every two of the sub-vectorscorresponding to the V_(b) parts are unequal.

It should be understood that, in the illustrated possible forms of thefirst codebook included in the first codebook set, i, j, k, l, m, n, p,and q are only for distinguishing different codebook vectors.

Further, in an embodiment of the present invention, V_(a) parts of allfirst sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in each first codebook form a sub-vector set {V_(K)}, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in each first codebook form a sub-vector set {V_(L)}, and thecorresponding {V_(K)} and {V_(L)} in the same first codebook meet afourth condition, where the fourth condition is: phase parts of asub-vector V_(k) in the {V_(k)} form a vector V_(k)′, vectors V_(k)′corresponding to all sub-vectors V_(k) in the {V_(k)} form a set{V_(k)′}, phase parts of a sub-vector V_(L) in the {V_(L)} form a vectorV_(L)′, vectors V_(L)′ corresponding to all sub-vectors V_(L) in the{V_(L)} form a set {V_(L)′}, and {V_(k)′}≠{V_(L)′} holds true. Accordingto concepts of sets, when a quantity of dimensions of the {V_(k)′} and aquantity of dimensions of the {V_(L)′} are unequal, {V_(k)′}≠{V_(L)′}holds true; when a quantity of dimensions of the {V_(k)′} and a quantityof dimensions of the {V_(L)′} are equal, but a quantity of sub-vectorsincluded in the {V_(k)′} and a quantity of sub-vectors included in the{V_(L)′} are unequal, {V_(k)′}≠{V_(L)′} holds true; or when a quantityof dimensions of the {V_(k)′} and a quantity of dimensions of the{V_(L)′} are equal, and a quantity of sub-vectors included in the{V_(k)′} and a quantity of sub-vectors included in the {V_(L)′} areequal, but the sub-vectors included in the {V_(k)′} are different fromthe sub-vectors included in the {V_(L)′}, {V_(k)′}≠{V_(L)′} also holdstrue.

In another embodiment of the present invention, when the value of the RIis greater than 1, V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in each first codebook form a sub-vector set {V_(M)}, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in each first codebook form a sub-vector set {V_(N)}, and thecorresponding {V_(M)} and {V_(N)} in the same first codebook meet afifth condition, where the fifth condition is: amplitude parts of asub-vector V_(M) in the {V_(M)} form a vector V_(M)′, vectors V_(M)′corresponding to all sub-vectors V_(M) in the {V_(M)} form a set{V_(M)′}, amplitude parts of a sub-vector V_(N) in the {V_(N)} form avector V_(N)′, vectors V_(N)′ corresponding to all sub-vectors V_(N) inthe {V_(N)} form a set {V_(N)′}, and {V_(M)′}≠{V_(N)′} holds true.According to concepts of sets, when a quantity of dimensions of the{V_(M)′} and a quantity of dimensions of the {V_(N)′} are unequal,{V_(M)′}≠{V_(N)′} holds true; when a quantity of dimensions of the{V_(M)′} and a quantity of dimensions of the {V_(N)′} are equal, but aquantity of sub-vectors included in the {V_(M)′} and a quantity ofsub-vectors included in the {V_(N)′} are unequal, {V_(M)′}≠{V_(N)′}holds true; or when a quantity of dimensions of the {V_(M)′} and aquantity of dimensions of the {V_(N)′} are equal, and a quantity ofsub-vectors included in the {V_(M)′} and a quantity of sub-vectorsincluded in the {V_(N)′} are equal, but the sub-vectors included in the{V_(M)′} are different from the sub-vectors included in the {V_(N)′},{V_(M)′}≠{V_(N)′} also holds true.

In the foregoing embodiment, with the first codebook that makes the{V_(k)′}≠{V_(L)′} and/or {V_(M)′}≠{V_(N)′} relation hold true, flexibleconfigurations of the first structure and the second structure areimplemented, and a codebook is better matched with a channel.

The following provides relationships of amplitude vectors respectivelycorresponding to

$\quad{\begin{bmatrix}V_{a} \\0\end{bmatrix}\mspace{14mu} {and}\mspace{14mu} {\quad{\begin{bmatrix}0 \\V_{b}\end{bmatrix}.}}}$

A first relationship of amplitude vectors, a second relationship ofamplitude vectors, and a third relationship of amplitude vectors eachprovide a configuration mode of a relationship between elements includedin each sub-vector. The third relationship of amplitude vectors and afourth relationship of amplitude vectors provide relationships betweendifferent codebook vectors in a codebook. The second network device mayconfigure different amplitude vectors according to channel conditions,so that transmission efficiency is higher. The definitions of amplitudevectors are already described, and are not further described herein.

For example, a codebook M₂ in a codebook set is:

$\begin{bmatrix}{a_{1}e^{{jw}_{1}}} & 0 & {b_{1}e^{j\; \theta_{1}}} & {c_{1}e^{j\; \gamma_{1}}} & 0 \\{a_{2}e^{{jw}_{2}}} & 0 & {b_{2}e^{j\; \theta_{2}}} & {c_{2}e^{j\; \gamma_{2}}} & 0 \\{a_{3}e^{{jw}_{3}}} & 0 & {b_{3}e^{j\; \theta_{3}}} & {c_{3}e^{j\; \gamma_{3}}} & 0 \\{a_{4}e^{{jw}_{4}}} & 0 & {b_{4}e^{j\; \theta_{4}}} & {c_{4}e^{j\; \gamma_{4}}} & 0 \\0 & {d_{1}e^{j\; \alpha_{1}}} & 0 & 0 & {g_{1}e^{j\; \beta_{1}}} \\0 & {d_{2}e^{j\; \alpha_{2}}} & 0 & 0 & {g_{2}e^{j\; \beta_{2}}}\end{bmatrix}.$

If M₂ meets the first relationship of amplitude vectors: at least twoelements in an amplitude vector in V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}\mspace{11mu}$

in the first codebook are unequal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}\mspace{11mu}$

in the first codebook are unequal, at least two values in a₁, a₂, a₃,and a₄ are unequal; at least two values in b₁, b₂, b₃, and b₄ areunequal; at least two values in c₁, c₂, c₃, and c₄ are unequal; d₁≠d₂;and g₁≠g₂.

If M₂ meets the second relationship of amplitude vectors: at least twoelements in an amplitude vector in V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}\mspace{11mu}$

in the first codebook are unequal, and all elements in an amplitudevector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}\mspace{11mu}$

in the first codebook are equal, at least two values in a₁, a₂, a₃, anda₄ are unequal; at least two values in b₁, b₂, b₃, and b₄ are unequal;at least two values in c₁, c₂, c₃, and c₄ are unequal; d₁≠d₂; and g₁=g₄.

If M₂ meets the third relationship of amplitude vectors: all elements inan amplitude vector in V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}\mspace{11mu}$

in the first codebook are equal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}\mspace{11mu}$

in the first codebook are unequal,

a₁=a₂=a₃=a₄; b₁=b₂=b₃=b₄; c₁=c₂=c₃=c₄; d₁≠d₂; and g₁≠g₂.

If M₂ meets the fourth relationship of amplitude vectors: at least twoamplitude vectors in a vector set formed by amplitude vectors in V_(a)of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}\mspace{11mu}$

in the first codebook are different, amplitude vectors in V_(a) of allcorresponding first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}\mspace{11mu}$

in M₂ are

$\begin{bmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4}\end{bmatrix},\begin{bmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4}\end{bmatrix},{{and}\mspace{14mu}\begin{bmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4}\end{bmatrix}},$

where at least two vectors of

$\begin{bmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4}\end{bmatrix},\begin{bmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4}\end{bmatrix},{{and}\mspace{14mu}\begin{bmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4}\end{bmatrix}}$

are different.

A fifth relationship of amplitude vectors is: at least two amplitudevectors in a vector set formed by amplitude vectors in V_(b) of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are different.

In this case, amplitude vectors in V_(b) of all corresponding secondsub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in M₂ are

$\quad{{\begin{bmatrix}d_{1} \\d_{2}\end{bmatrix}\mspace{14mu} {{and}\mspace{14mu}\begin{bmatrix}g_{1} \\g_{2}\end{bmatrix}}},{{{where}\mspace{14mu}\begin{bmatrix}d_{1} \\d_{2}\end{bmatrix}}\mspace{14mu} {{and}\mspace{14mu}\begin{bmatrix}g_{1} \\g_{2}\end{bmatrix}}}}$

are unequal.

FIG. 8 shows an embodiment of a first network-side apparatus accordingto the present invention, where the first network-side apparatusincludes: a receiver 301, configured to receive a reference signal; ameasurement unit 302, configured to measure the reference signal toobtain a measurement result; a selection unit 303, configured to selecta first codebook from a first codebook set according to the measurementresult; where the first codebook set includes at least two firstcodebooks, a sub-vector W_(x) of each first codebook is formed by a zerovector and a non-zero vector, and the vectors forming the W_(x)correspond to different groups of antenna ports; in each first codebook,different sub-vectors W_(x) are formed according to a same structure ordifferent structures; formation according to the same structure is: fordifferent sub-vectors W_(x)(1) and W_(x)(2), a location of a non-zerovector in the W_(x)(1) is the same as a location of a non-zero vector inthe W_(x)(2); and formation according to different structures is: fordifferent sub-vectors W_(x)(1) and W_(x)(2), a location of a non-zerovector in the W_(x)(1) is different from a location of a non-zero vectorin the W_(x)(2); and a sending unit 304, configured to send a codebookindex to a second network device, where the codebook index correspondsthe first codebook selected from the first codebook set.

Further, the codebook index is used to indicate the first codebook usedby the second network device in a coding and/or decoding process.

It should be understood that, in the present invention, a zero vectormay be a zero element with a length of 1, and a non-zero vector may be anon-zero element with a length of 1. Generally, for a passive antenna, adowntilt in a vertical direction is fixed. Therefore, for multiplespatially multiplexed data streams, adjustments can be made to multiplehorizontal beams only in a plane with a fixed downtilt in the verticaldirection, and the multiple data streams cannot be multiplexed morefreely in planes with multiple downtilts. In addition, if antenna portsare grouped according to different downtilts, a codebook structureprovided by the present invention may be configured independentlyaccording to transmit power of different groups of antenna ports, sothat flexibility and MIMO performance are improved.

In an embodiment of the present invention, when antenna ports aregrouped according to tilts in the vertical direction, parameters ofcodebook vectors in a codebook may be configured independently accordingto different tilts, so that an objective of flexibly adapting to datatransmission efficiency is achieved. In this embodiment, two tilts inthe vertical direction are used as an example (this method is alsoapplicable to more than two tilts). In each column in the firstcodebook, one group of antenna ports corresponds to a non-zero vector,and another group of antenna ports corresponds to a zero vector; or onegroup of antenna ports corresponds to a zero vector, and another groupof antenna ports corresponds to a non-zero vector, where the non-zerovector refers to a vector in which at least one element is a non-zeroelement, and the zero vector refers to a vector in which all elementsare zero elements. In the present invention, when first n1 elements in avector included in a codebook correspond to one group of antenna ports,and last n2 elements correspond to another group of antenna ports, astructure of this vector is

$\quad{\begin{bmatrix}V_{1} \\V_{2}\end{bmatrix},}$

where V₁ is n1-dimensional, and V₂ is n2-dimensional. In this case, eachfirst codebook includes at least one first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

having a first structure and/or at least one second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

having a second structure; where V_(a) in

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

is an n1-dimensional non-zero vector and corresponds to a first group ofantenna ports; 0 in

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

represents an n2-dimensional zero vector and corresponds to a secondgroup of antenna ports; V_(b) in

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

is an n2-dimensional non-zero vector and corresponds to the second groupof antenna ports; and 0 in

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

represents an n1-dimensional zero vector and corresponds to the firstgroup of antenna ports. It should be understood that, the presentinvention is not limited to the case of grouping into only two groups.In an actual application, antenna ports are grouped into more groupsaccording to other factors such as different downtilts or signal qualityor the like. In a specific measurement process, codebooks in the firstcodebook set are traversed, so that a first codebook that best matches atransmission characteristic is determined and used for channeltransmission.

It should be understood that, the structure of the sub-vector in thefirst codebook may be but is not limited to the foregoing firststructure or the second structure. Optionally, locations of sub-vectorsof the zero vector and the non-zero vector in the first codebook may bedifferent. In an embodiment of the present invention, in a case of fourantenna ports, elements in vectors in the first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

having the first structure are represented as

$\quad\begin{bmatrix}V_{a}^{0} \\V_{a}^{1} \\0 \\0\end{bmatrix}$

and elements in vectors in the second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

having the second structure are represented as

$\quad{\begin{bmatrix}0 \\0 \\V_{b}^{0} \\V_{b}^{1}\end{bmatrix},}$

where V_(a) ⁰ and V_(a) ¹ are elements in the vector V_(a), and V_(b) ⁰and V_(b) ¹ are elements in the vector V_(b). In another embodiment ofthe present invention, when the antenna ports are grouped into twogroups, the first structure may be

$\quad{\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix},}$

and the second structure may be

$\quad{\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix}.}$

Likewise, when the antenna groups are grouped into two groups, inanother embodiment of the present invention, the first structure may be

$\quad{\begin{bmatrix}V_{a}^{0} \\0 \\0 \\V_{a}^{1}\end{bmatrix},}$

and the second structure may be

$\quad{\begin{bmatrix}0 \\V_{b}^{0} \\V_{b}^{1} \\0\end{bmatrix}.}$

Alternatively, the first codebook set includes at least one of thefollowing four structures: a first structure

$\quad{\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix},}$

a second structure

$\quad{\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix},}$

a third structure

$\quad{\begin{bmatrix}V_{a}^{0} \\0 \\0 \\V_{a}^{1}\end{bmatrix},}$

or a fourth structure

$\quad{\begin{bmatrix}0 \\V_{b}^{0} \\V_{b}^{1} \\0\end{bmatrix}.}$

V_(a) ⁰ and V_(a) ¹ are elements in the vector V_(a), and Va correspondsto one group of antenna ports. A correspondence is as follows: In thefirst structure, V_(a) ⁰ corresponds to a first antenna port, and V_(a)¹ corresponds to a third antenna port; in the second structure, V_(b) ⁰corresponds to a second antenna port, and V_(b) ¹ corresponds to afourth antenna port; in the third structure, V_(a) ⁰ corresponds to thefirst antenna port, and V_(a) ¹ corresponds to the fourth antenna port;in the fourth structure, V_(b) ⁰ corresponds to the second antenna port,and V_(b) ¹ corresponds to the third antenna port, where V_(a) ⁰ andV_(a) ¹ are elements in the vector V_(a), and V_(b) ⁰ and V_(b) ¹ areelements in the vector V_(b).

When the antenna ports are grouped into three groups, the first codebookset includes at least one of a first structure

$\quad{\begin{bmatrix}V_{a} \\0 \\0\end{bmatrix},}$

a second structure

$\quad{\begin{bmatrix}0 \\V_{b} \\0\end{bmatrix},}$

a third structure

$\quad{\begin{bmatrix}0 \\0 \\V_{c}\end{bmatrix},}$

a fourth structure

$\quad{\begin{bmatrix}V_{a} \\0 \\V_{c}\end{bmatrix},}$

a fifth structure

$\quad{\begin{bmatrix}V_{a} \\V_{b} \\0\end{bmatrix},}$

or a sixth structure

$\quad{\begin{bmatrix}0 \\V_{b} \\V_{c}\end{bmatrix}.}$

Vectors V_(a), V_(b), and V_(c) each correspond to one group of antennaports.

In an embodiment of the present invention, the present inventionprovides a combination of the first structure and the second structurecorresponding to a value of the rank indicator.

Generally, an element in a non-zero vector included in the firstcodebook is in a form of a complex number. For a complex number α·e^(β),α is referred to as an amplitude part, and is a real number, and e^(β)is referred to as a phase part. In still another embodiment of thepresent invention, at least one first codebook meets a first condition.The present invention provides several definitions of the firstcondition that can be implemented. In the present invention, unlessotherwise limited, P, Q, and K are any positive integers.

First Definition of the First Condition:

A vector set formed by all first phase vectors and a discrete Fouriertransform matrix DFT matrix meet a first correspondence that the vectorset formed by the first phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the DFT matrix, wherean element in a P^(th) row and a Q^(th) column in the phase matrix ofthe DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the first phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding first phase vector, where P, Q, and K areany positive integers.

A general expression of the discrete Fourier transform matrix DFT matrixis:

$M_{dft} = {{\frac{1}{\sqrt{N}}\begin{bmatrix}1 & 1 & 1 & 1 & \ldots & 1 \\1 & \omega & \omega^{2} & \omega^{3} & \ldots & \omega^{N - 1} \\1 & \omega^{2} & \omega^{4} & \omega^{6} & \ldots & \omega^{2{({N - 1})}} \\1 & \omega^{3} & \omega^{6} & \omega^{9} & \ldots & \omega^{3{({N - 1})}} \\M & M & M & M & \; & M \\1 & \omega^{N - 1} & \omega^{2{({N - 1})}} & \omega^{3{({N - 1})}} & \ldots & \omega^{{({N - 1})}{({N - 1})}}\end{bmatrix}}.}$

The phase matrix of the DFT matrix is:

$M_{{dft}\; \_ \; {phase}} = {\begin{bmatrix}1 & 1 & 1 & 1 & \ldots & 1 \\1 & \omega & \omega^{2} & \omega^{3} & \ldots & \omega^{N - 1} \\1 & \omega^{2} & \omega^{4} & \omega^{6} & \ldots & \omega^{2{({N - 1})}} \\1 & \omega^{3} & \omega^{6} & \omega^{9} & \ldots & \omega^{3{({N - 1})}} \\M & M & M & M & \; & M \\1 & \omega^{N - 1} & \omega^{2{({N - 1})}} & \omega^{3{({N - 1})}} & \ldots & \omega^{{({N - 1})}{({N - 1})}}\end{bmatrix}.}$

A value of N is an order in a case in which the DFT matrix is a squarematrix. For example, in

$\quad{\begin{bmatrix}V_{a} \\0\end{bmatrix},}$

if V_(a) is four-dimensional, the order of the phase matrix of the DFTmatrix is 4. In an embodiment, a value of ω may be

$\omega = e^{j\frac{2\pi}{N}}$

$M_{{dft}\; \_ \; {phase}\; \_ 4} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & \omega & \omega^{2} & \omega^{3} \\1 & \omega^{2} & \omega^{4} & \omega^{6} \\1 & \omega^{3} & \omega^{6} & \omega^{9}\end{bmatrix}.}$

For example, when the value of ω is e

$e^{j\; \frac{2\pi}{32}},$

a form of a fourth-order DFT matrix

$M_{{dft}\; \_ \; {phase}\; \_ \; 4\_ \; e^{j\; \frac{2\pi}{32}}}$

is:

$M_{{dft}\; \_ \; {phase}\; \_ \; 4\_ \; e^{j\; \frac{2\pi}{32}}} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & e^{j\; \frac{2\pi}{32}} & e^{2j\; \frac{2\pi}{32}} & e^{3j\; \frac{2\pi}{32}} \\1 & e^{2j\frac{2\pi}{32}} & e^{4j\; \frac{2\pi}{32}} & e^{6j\; \frac{2\pi}{32}} \\1 & e^{3j\; \frac{2\pi}{32}} & e^{6j\; \frac{2\pi}{32}} & e^{9j\; \frac{2\pi}{32}}\end{bmatrix}.}$

Correspondingly, the set of corresponding columns in the phase matrix ofthe DFT matrix is:

$\left\{ V_{m}^{\prime} \right\} = {\left\{ {\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\e^{j\; \frac{2\pi}{32}} \\e^{2j\; \frac{2\pi}{32}} \\e^{3j\; \frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{2j\; \frac{2\pi}{32}} \\e^{4j\; \frac{2\pi}{32}} \\e^{6j\; \frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{3j\; \frac{2\pi}{32}} \\e^{6j\; \frac{2\pi}{32}} \\e^{9j\; \frac{2\pi}{32}}\end{bmatrix}} \right\}.}$

It should be understood that, in the present invention, the phase matrixof the DFT matrix is not necessarily a square matrix. More columns orrows may be selected according to an order. For example, the matrix maybe:

$M_{{dft}\; \_ \; {phase}\; \_ \; 4\_ \; e^{j\; \frac{2\pi}{32}}}^{\prime} = {\begin{bmatrix}1 & 1 & 1 & 1 & 1 \\1 & e^{j\; \frac{2\pi}{32}} & e^{2j\; \frac{2\pi}{32}} & e^{3j\; \frac{2\pi}{32}} & e^{4j\; \frac{2\pi}{32}} \\1 & e^{2j\frac{2\pi}{32}} & e^{4j\; \frac{2\pi}{32}} & e^{6j\; \frac{2\pi}{32}} & e^{8j\; \frac{2\pi}{32}} \\1 & e^{3j\; \frac{2\pi}{32}} & e^{6j\; \frac{2\pi}{32}} & e^{9j\; \frac{2\pi}{32}} & e^{12j\; \frac{2\pi}{32}}\end{bmatrix}.}$

The set of corresponding columns in the phase matrix of the DFT matrixis:

$\left\{ V_{m}^{\prime} \right\} = {\left\{ {\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\e^{j\; \frac{2\pi}{32}} \\e^{2j\; \frac{2\pi}{32}} \\e^{3j\; \frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{2j\; \frac{2\pi}{32}} \\e^{4j\; \frac{2\pi}{32}} \\e^{6j\; \frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{3j\; \frac{2\pi}{32}} \\e^{6j\; \frac{2\pi}{32}} \\e^{9j\; \frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{4j\; \frac{2\pi}{32}} \\e^{8j\; \frac{2\pi}{32}} \\e^{12j\; \frac{2\pi}{32}}\end{bmatrix}} \right\}.}$

It should be understood that, a quantity of rows or a quantity ofcolumns selected from the DFT matrix is not limited in the presentinvention. It should be understood that, the quantity of rows should beat least the same as a value of V_(a), and the quantity of columnsshould be at least the same as a quantity of first vectors in acodebook.

Second Definition of the First Condition:

A vector set formed by all second phase vectors and at least one CMPcodebook in a CMP codebook set meet a second correspondence that thevector set formed by the second phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the CMP codebookmatrix, where an element in a P^(th) row and a Q^(th) column in thephase matrix of the CMP codebook matrix is a phase part of an element ina P^(th) row and a Q^(th) column in the CMP codebook matrix, V_(a) partsof all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the second phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding second phase vector, where P, Q, and K areany positive integers, and the CMP codebook refers to a codebook inwhich only one layer in layers corresponding to each port is a non-zeroelement.

In all CMP codebooks, CMP codebooks in which column vectors aretwo-dimensional are:

TABLE 1 Quantity of layers Codebook index v = 1 v = 2 0$\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ 1 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}$ — 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}$ — 3 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}$ — 4 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\0\end{bmatrix}$ — 5 $\frac{1}{\sqrt{2}}\begin{bmatrix}0 \\1\end{bmatrix}$ —

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 1 are:

TABLE 2 Codebook Quantity of layers index v = 1 0-7$\frac{1}{2}\begin{bmatrix}1 \\1 \\1 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\j \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\{- 1} \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\{- j} \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\1 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\j \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\{- 1} \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\{- j} \\{- 1}\end{bmatrix}$  8-15 $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\1 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\j \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\{- 1} \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\{- j} \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\1 \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\j \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\{- 1} \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\{- j} \\1\end{bmatrix}$ 16-23 $\frac{1}{2}\begin{bmatrix}1 \\0 \\1 \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\{- 1} \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\j \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\{- j} \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\{- j}\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 2 are:

TABLE 3 Codebook Quantity of layers index v = 2 0-3$\frac{1}{2}\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}$ 4-7 $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}$  8-11 $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & {- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & {- 1}\end{bmatrix}$ 12-15 $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 1 \\1 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & {- 1} \\1 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 1 \\{- 1} & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & {- 1} \\{- 1} & 0\end{bmatrix}$

For example, when the index in Table 3 is 0, the subset of the set ofcorresponding column vectors in the phase matrix of the correspondingCMP codebook matrix is:

$\left\{ {\begin{bmatrix}e^{0} \\e^{0} \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\e^{0} \\e^{{- j}\frac{\pi}{2}}\end{bmatrix}} \right\}.$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 3 are:

TABLE 4 Code- book Quantity of layers index v = 3 0-3$\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\{- 1} & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\{- 1} & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ 4-7 $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\{- 1} & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\{- 1} & 0 & 0 \\0 & 0 & 1\end{bmatrix}$  8-11 $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1 \\{- 1} & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0 \\{- 1} & 0 & 0\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 4 are:

TABLE 5 Quantity of layers Codebook index v = 4 0$\frac{1}{2}\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}$

Third Definition of the First Condition:

A vector set formed by all third phase vectors is a subset of a setformed by corresponding sub-vectors in a householder transform codebook,where a householder transform expression is W_(n)=I−u_(n)u_(n)^(H)/u_(n) ^(H)u_(n).

V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the third phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding third phase vector.

For example, the third phase vectors are a subset of a set formed byphase parts of W_(index) ^({α) ^(i) ^(}) in a matrix corresponding todifferent quantities of layers and different codebook indexes in Table6. The index corresponds to different codebook indexes. {α_(i)}corresponds to an integer set, and is used to indicate that differentcolumns in W_(index) ^({α) ^(i) ^(}) are selected as third phasevectors. In Table 6, U_(n) is a corresponding U_(n) in the householdertransform, and I is a unit matrix.

It should be understood that, in the present invention, a value of theV_(a) is not limited only to cases or relationships shown in the firstdefinition of the first condition, the second definition of the firstcondition, and the third definition of the first condition. The codebookmay further be a codebook defined for two antennas, four antennas, oreight antennas in LTE.

TABLE 6 Codebook Number of layers ν index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1−1]^(T) W₀ ^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{squareroot over (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁^({12})/{square root over (2)} W₁ ^({123})/{square root over (3)} W₁^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over(2)} W₂ ^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1−j]^(T) W₃ ^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{squareroot over (3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)}−j (1 − j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square rootover (2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1− j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

In still another embodiment of the present invention, at least one firstcodebook meets a second condition. The present invention providesseveral definitions of the second condition that can be implemented.

First Definition of the Second Condition:

A vector set formed by all fourth phase vectors and a discrete Fouriertransform matrix DFT matrix meet a third correspondence that the vectorset formed by the fourth phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the DFT matrix, wherean element in a P^(th) row and a Q^(th) column in the phase matrix ofthe DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fourth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fourth phase vector.

Second Definition of the Second Condition:

A vector set formed by all fifth phase vectors and at least one CMPcodebook in a CMP codebook set meet a fourth correspondence that thevector set formed by the fifth phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the CMP codebookmatrix, where an element in a P^(th) row and a Q^(th) column in thephase matrix of the CMP is a phase part of an element in a P^(th) rowand a Q^(th) column in the CMP codebook matrix, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fifth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fifth phase vector, where P, Q, and K areany positive integers.

Third Definition of the Second Condition:

A vector set formed by all sixth phase vectors is a set formed bycorresponding sub-vectors in a householder transform codebook, whereV_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the sixth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding sixth phase vector.

It should be understood that, in the present invention, a value of theV_(b) is not limited only to cases or relationships shown in the firstdefinition of the second condition, the second definition of the secondcondition, and the third definition of the second condition. The presentinvention requests to protect correspondences according to the secondcondition: a relationship between the fourth phase vectors and differentDFT matrices formed by different parameters, a relationship between thefifth phase vectors and the CMP codebook set, and a relationship betweenthe sixth phase vectors and the householder codebook formed by differentoriginal vectors through householder transforms.

It should be understood that, due to independence, in one codebook, whenthe first codebook meets any definition of the first condition, a secondcodebook may meet any definition of the second condition. For example,in the first codebook, that the vector set formed by the first phasevectors is the subset of the set of corresponding column vectors in thephase matrix of the DFT matrix is met; in the second codebook, that thevector set formed by the fifth phase vectors is the subset of the set ofcorresponding column vectors in the phase matrix of the CMP codebookmatrix, or any combination thereof is met.

In still another embodiment of the present invention, at least one firstcodebook meets a third condition:

In all first amplitude vectors corresponding to {V_(m)}, at least onefirst amplitude vector is different from all second amplitude vectorscorresponding to the {V_(n)}; and/or in all second amplitude vectorscorresponding to the {V_(n)}, at least one second amplitude vector isdifferent from all first amplitude vectors corresponding to the {V_(m)}.V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form the set {V_(m)}, amplitude parts of allelements in each sub-vector of the {V_(m)} form the first amplitudevector, and a phase part of a K^(th) element in each sub-vector of the{V_(m)} is a K^(th) element of each corresponding first amplitudevector; and V_(b) parts of all second sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook form the set {V_(n)}, amplitude parts of allelements in each sub-vector of the {V_(n)} form the second amplitudevector, and an amplitude part of a K^(th) element in each sub-vector ofthe {V_(n)} is a K^(th) element of each corresponding second amplitudevector. In this embodiment, in a sub-vector included in each firstcodebook, an amplitude part of each element corresponds to power of anantenna port. In this embodiment, in a sub-vector included in each firstcodebook, amplitude vectors of each group of antenna ports aredetermined independently according to tilt characteristics of this groupof antenna ports (tilts may be classified into electrical tilts andmechanical tilts; an electrical tilt means that weighted vectors ofmultiple antenna elements corresponding to one antenna port make themultiple antenna elements form a beam pointing to a tilt). For example,all tilts of the first group of antenna ports are 12 degrees, and alltilts of the second group of antenna ports are 3 degrees; it is assumedthat a horizontal plane is 0 degrees and that those downward arepositive tilts. In this case, energies received from the two groups ofantenna ports by the first network device in a location are different.Therefore, independent control may be performed on amplitudes ofcodebooks of the two groups of antenna ports, so that receptionperformance is optimized.

In an embodiment of the present invention, FIG. 9 further shows a thirdacquiring unit 305, configured to acquire the first codebook set beforethe first codebook is selected. In another embodiment of the presentinvention, FIG. 10 shows a memory 306, configured to pre-store the firstcodebook set in the first network device.

Optionally, FIG. 11 further shows a second receiving unit 307,configured to receive at least one first configuration message, whereeach first configuration message is used to determine a sub-vector setof phase parts corresponding to one group of antenna ports, and aquantity of the at least one first configuration message is equal to aquantity of groups of the antenna ports; and/or a third receiving unit308, configured to receive at least one second configuration message,where each second configuration message is used to determine asub-vector set of amplitude parts corresponding to one group of antennaports, and a quantity of the at least one second configuration messageis equal to a quantity of groups of the antenna ports. In an embodiment,the first configuration message is configured by the second networkdevice by using higher layer signaling or dynamic signaling; and/or thesecond configuration message is configured by the second network deviceby using higher layer signaling or dynamic signaling. In anotherembodiment, the first configuration message is obtained by the firstnetwork device by measuring the reference signal; and/or the secondconfiguration message is obtained by the first network device bymeasuring the reference signal.

In an embodiment, the present invention provides possible cases of acodebook set having the first structure and the second structure. Itshould be understood that, the first codebook that the present inventionrequests to protect may be but is not limited to the followingstructures:

1. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} \\0\end{bmatrix}\mspace{14mu} {or}\mspace{14mu} {\quad{\begin{bmatrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{bmatrix},}}$

where a value of a rank indicator is 1, a non-zero sub-vectorrepresented by V_(a)(x) is a sub-vector in the first vector set {V_(m)}and has a sequence number x, a non-zero sub-vector represented byV_(b)(y) is a sub-vector in the first vector set {V_(n)} and has asequence number y, 0<i≤N₁, and 0<i′≤N₁, where N₁ represents a quantityof sub-vectors in the {V_(m)}, and N₁′ represents a quantity ofsub-vectors in the {V_(n)}; or

2. the first codebook is one of the following matrices:

$\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} \\0 & 0\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},{{or}\mspace{14mu} {\quad{\begin{bmatrix}0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},}}}}}}}}$

where a value of a rank indicator is 2, 0<i≤N₁, 0<i′≤N₁, 0<j N₁, and0<j′≤N₁; or

3. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\0 & 0 & 0\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},{{or}\mspace{14mu}\begin{bmatrix}0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}},}}}}}}}}$

where a value of a rank indicator is 3, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, and 0<k′≤N₁; or

4. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & 0 & 0\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},{\quad {\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad {\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},{{or}\mspace{14mu}\begin{bmatrix}0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}},}}}}}}}}}}}}}}$

where a value of a rank indicator is 4, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, and 0<l′≤N₁; or

5. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & 0 & 0\end{bmatrix},{\quad {\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},{\quad {\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},{\quad {\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},{\quad {\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},{\quad{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(1)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(1)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(4)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(1)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},}}}}}}}}}}}}}}$

where a value of a rank indicator is 5, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, and 0<m′≤N₁; or

6. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & 0\end{bmatrix},{\quad {\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},{\quad {\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix},{\quad {\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},{\quad {\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},{\quad{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(5)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(1)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},{\quad {\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad {\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}(j)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}(i)} & {V_{b}(j)} & 0 & {V_{b}(k)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad {\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad {\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},\mspace{14mu} \begin{matrix}{\mspace{11mu} {\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},{or}}} \\{\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack,}\end{matrix}}\;}}}}}}}}}}}}}}}}}}}}}}}}}}}$

where a value of a rank indicator is 6, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁, and0<n′≤N₁; or

7. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\quad{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}$

$ {\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}{\quad{\quad{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(4)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack}}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\quad{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}{\quad{\quad{{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack},}}}}}}}}}}}}}}}$

where a value of a rank indicator is 7, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁,0<n′≤N₁, 0<p≤N₁, and 0<p′≤N₁; or

8. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} & {V_{a}(q)} \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}{\quad{{{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}(2)} & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}(2)} & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0 & 0\end{matrix} \right\rbrack}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{{{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}{\quad{{{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{matrix} \right\rbrack}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}(i)} & 0 & {V_{b}(j)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{{{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0 & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}{\quad{{{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{{{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}$

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}{\quad{{{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)} & 0\end{matrix} \right\rbrack}}}}}}}}}}$

$\quad\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}{\quad{{{{{{{{{{{{{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{a}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)} & {V_{b}\left( q^{\prime} \right)}\end{matrix} \right\rbrack}}}}}}}}}}$

where a value of a rank indicator is 8, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, and 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁,0<n′≤N₁, 0<p≤N₁, 0<p′≤N₁, 0<q≤N₁, and 0<q′≤N₁, where for parameters ofi, j, k, l, m, n, p, q, and the like, every two of the sub-vectorscorresponding to the V_(a) parts are unequal, and for parameters of i′,j′, k′, l′, m′, n′, p′, q′, and the like, every two of the sub-vectorscorresponding to the V_(b) parts are unequal.

It should be understood that, in the illustrated possible forms of thefirst codebook included in the first codebook set, i, j, k, l, m, n, p,and q are only for distinguishing locations of different codebookvectors.

Further, in an embodiment of the present invention, V_(a) parts of allfirst sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in each first codebook form a sub-vector set {V_(K)}, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in each first codebook form a sub-vector set {V_(L)}, and thecorresponding {V_(K)} and {V_(L)} in the same first codebook meet afourth condition, where the fourth condition is: phase parts of asub-vector V_(k) in the {V_(k)} form a vector V_(k)′, vectors V_(k)′corresponding to all sub-vectors V_(k) in the {V_(k)} form a set{V_(k)′}, phase parts of a sub-vector V_(L) in the {V_(L)} form a vectorV_(L)′, vectors V_(L)′ corresponding to all sub-vectors V_(L) in the{V_(L)} form a set {V_(L)′}, and {V_(k)′}≠{V_(L)′} holds true. Accordingto concepts of sets, when a quantity of dimensions of the {V_(k)′} and aquantity of dimensions of the {V_(L)′} are unequal, {V_(k)′}≠{V_(L)′}holds true; when a quantity of dimensions of the {V_(k)′} and a quantityof dimensions of the {V_(L)′} are equal, but a quantity of sub-vectorsincluded in the {V_(k)′} and a quantity of sub-vectors included in the{V_(L)′} are unequal, {V_(k)′}≠{V_(L)′} holds true; or when a quantityof dimensions of the {V_(k)′} and a quantity of dimensions of the{V_(L)′} are equal, and a quantity of sub-vectors included in the{V_(k)′} and a quantity of sub-vectors included in the {V_(L)′} areequal, but the sub-vectors included in the {V_(k)′} are different fromthe sub-vectors included in the {V_(L)′}, {V_(k)′}≠{V_(L)′} also holdstrue.

In another embodiment of the present invention, when the value of the RIis greater than 1, V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in each first codebook form a sub-vector set {V_(M)}, V_(b) parts of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in each first codebook form a sub-vector set {V_(N)}, and thecorresponding {V_(M)} and {V_(N)} in the same first codebook meet afifth condition, where the fifth condition is: amplitude parts of asub-vector V_(M) in the {V_(M)} form a vector V_(M)′, vectors V_(M)′corresponding to all sub-vectors V_(M) in the {V_(M)} form a set{V_(M)′}, amplitude parts of a sub-vector V_(N) in the {V_(N)} form avector V_(N)′, vectors V_(N)′ corresponding to all sub-vectors V_(N) inthe {V_(N)} form a set {V_(N)′}, and {V_(M)′}≠{V_(N)′} holds true.According to concepts of sets, when a quantity of dimensions of the{V_(M)′} and a quantity of dimensions of the {V_(N)′} are unequal,{V_(M)′}≠{V_(N)′} holds true; when a quantity of dimensions of the{V_(M)′} and a quantity of dimensions of the {V_(N)′} are equal, but aquantity of sub-vectors included in the {V_(M)′} and a quantity ofsub-vectors included in the {V_(N)′} are unequal, {V_(M)′}≠{V_(N)′}holds true; or when a quantity of dimensions of the {V_(M)′} and aquantity of dimensions of the {V_(N)′} are equal, and a quantity ofsub-vectors included in the {V_(M)′} and a quantity of sub-vectorsincluded in the {V_(N)′} are equal, but the sub-vectors included in the{V_(M)′} are different from the sub-vectors included in the {V_(N)′},{V_(M)′}≠{V_(N)′} also holds true.

In the foregoing embodiment, with the first codebook that makes the{V_(k)′}≠{V_(L)′} and/or {V_(M)′}≠{V_(N)′} relation hold true, flexibleconfigurations of the first structure and the second structure areimplemented, and a codebook is better matched with a channel.

The following provides relationships of amplitude vectors respectivelycorresponding to

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\mspace{14mu} {{{and}\mspace{14mu}\begin{bmatrix}0 \\V_{b}\end{bmatrix}}.}$

A first relationship of amplitude vectors, a second relationship ofamplitude vectors, and a third relationship of amplitude vectors eachprovide a configuration mode of a relationship between elements includedin each sub-vector. The third relationship of amplitude vectors and afourth relationship of amplitude vectors provide relationships betweendifferent codebook vectors in a codebook. The second network device mayconfigure different amplitude vectors according to channel conditions,so that transmission efficiency is higher. The definitions of amplitudevectors are already described, and are not further described herein.

For example, a codebook M₂ in a codebook set is:

$\begin{bmatrix}{a_{1}e^{{jw}_{1}}} & 0 & {b_{1}e^{j\; \theta_{1}}} & {c_{1}e^{j\; \gamma_{1}}} & 0 \\{a_{2}e^{{jw}_{1}}} & 0 & {b_{2}e^{j\; \theta_{2}}} & {c_{2}e^{j\; \gamma_{2}}} & 0 \\{a_{3}e^{{jw}_{1}}} & 0 & {b_{3}e^{j\; \theta_{3}}} & {c_{3}e^{j\; \gamma_{3}}} & 0 \\{a_{4}e^{{jw}_{1}}} & 0 & {b_{4}e^{j\; \theta_{4}}} & {c_{4}e^{j\; \gamma_{4}}} & 0 \\0 & {d_{1}e^{j\; \alpha_{1}}} & 0 & 0 & {g_{1}e^{j\; \beta_{1}}} \\0 & {d_{2}e^{j\; \alpha_{2}}} & 0 & 0 & {g_{1}e^{j\; \beta_{2}}}\end{bmatrix}.$

If M₂ meets the first relationship of amplitude vectors: at least twoelements in an amplitude vector in V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are unequal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are unequal; at least two values in a₁, a₂, a₃,and a₄ are unequal; at least two values in b₁, b₂, b₃, and b₄ areunequal; at least two values in c₁, c₂, c₃, and c₄ are unequal; d₁≠d₂;and g₁≠g₂.

If M₂ meets the second relationship of amplitude vectors: at least twoelements in an amplitude vector in V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are unequal, and all elements in an amplitudevector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are equal, at least two values in a₁, a₂, a₃, anda₄ are unequal; at least two values in b₁, b₂, b₃, and b₄ are unequal;at least two values in c₁, c₂, c₃, and c₄ are unequal; d₁≠d₂; and g₁=g₄.

If M₂ meets the third relationship of amplitude vectors: all elements inan amplitude vector in V_(a) of each first sub-vector

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are equal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are unequal, a₁=a₂=a₃=a₄; b₁=b₂=b₃=b₄;c₁=c₂=c₃=c₄; d₁≠d₂; and g₁≠g₂.

If M₂ meets the fourth relationship of amplitude vectors: at least twoamplitude vectors in a vector set formed by amplitude vectors in V_(a)of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook are different, amplitude vectors in V_(a) of allcorresponding first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in M₂ are

$\begin{bmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4}\end{bmatrix},\begin{bmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4}\end{bmatrix},{{and}\mspace{14mu}\begin{bmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4}\end{bmatrix}},$

where at least two vectors of

$\begin{bmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4}\end{bmatrix},\begin{bmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4}\end{bmatrix},{{and}\mspace{14mu}\begin{bmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4}\end{bmatrix}}$

are different.

A fifth relationship of amplitude vectors is: at least two amplitudevectors in a vector set formed by amplitude vectors in V_(b) of allsecond sub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in the first codebook are different.

In this case, amplitude vectors in V_(b) of all corresponding secondsub-vectors

$\quad\begin{bmatrix}0 \\V_{b}\end{bmatrix}$

in M₂ are

${\begin{bmatrix}d_{1} \\d_{2}\end{bmatrix}\mspace{14mu} {{and}\mspace{14mu}\begin{bmatrix}g_{1} \\g_{2}\end{bmatrix}}},{{{where}\mspace{14mu}\begin{bmatrix}d_{1} \\d_{2}\end{bmatrix}}\mspace{14mu} {{and}\mspace{14mu}\begin{bmatrix}g_{1} \\g_{2}\end{bmatrix}}}$

are unequal.

FIG. 12 shows an embodiment of a second network-side device according tothe present invention, where the second network-side device includes: afirst sending unit 401, configured to send a reference signal to a firstnetwork device, where the reference signal is used to notify the firstnetwork device to perform a measurement to obtain a measurement result;

a receiving unit 402, configured to receive a codebook index sent by thefirst network device, where the codebook index corresponds to a firstcodebook determined in the first codebook set by the first networkdevice, and the codebook index is determined by the first network deviceaccording to the measurement result; and a determining unit 403,configured to determine, according to the codebook index, the firstcodebook in the first codebook set; where the first codebook setincludes at least two first codebooks, a sub-vector W_(x) of each firstcodebook is formed by a zero vector and a non-zero vector, and thevectors forming the W_(x) correspond to different groups of antennaports; in each first codebook, different sub-vectors W_(x) are formedaccording to a same structure or different structures; formationaccording to the same structure is: for different sub-vectors W_(x)(1)and W_(x)(2), a location of a non-zero vector in the W_(x)(1) is thesame as a location of a non-zero vector in the W_(x)(2); and formationaccording to different structures is: for different sub-vectors W_(x)(1)and W_(x)(2), a location of a non-zero vector in the W_(x)(1) isdifferent from a location of a non-zero vector in the W_(x)(2).

It should be understood that, in the present invention, a zero vectormay be a zero element with a length of 1, and a non-zero vector may be anon-zero element with a length of 1. Generally, for a passive antenna, adowntilt in a vertical direction is fixed. Therefore, for multiplespatially multiplexed data streams, adjustments can be made to multiplehorizontal beams only in a plane with a fixed downtilt in the verticaldirection, and the multiple data streams cannot be multiplexed morefreely in planes with multiple downtilts. In addition, if antenna portsare grouped according to different downtilts, a codebook structureprovided by the present invention may be configured independentlyaccording to transmit power of different groups of antenna ports, sothat flexibility and MIMO performance are improved.

In an embodiment of the present invention, when antenna ports aregrouped according to tilts in the vertical direction, parameters ofcodebook vectors in a codebook may be configured independently accordingto different tilts, so that an objective of flexibly adapting to datatransmission efficiency is achieved. In this embodiment, two tilts inthe vertical direction are used as an example (this method is alsoapplicable to more than two tilts). In each column in the firstcodebook, one group of antenna ports corresponds to a non-zero vector,and another group of antenna ports corresponds to a zero vector; or onegroup of antenna ports corresponds to a zero vector, and another groupof antenna ports corresponds to a non-zero vector, where the non-zerovector refers to a vector in which at least one element is a non-zeroelement, and the zero vector refers to a vector in which all elementsare zero elements. In the present invention, when first n1 elements in avector included in a codebook correspond to one group of antenna ports,and last n2 elements correspond to another group of antenna ports, astructure of this vector is

$\begin{bmatrix}V_{1} \\V_{2}\end{bmatrix},$

where V₁ is n1-dimensional, and V₂ is n2-dimensional. In this case, eachfirst codebook includes at least one first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

having a first structure and/or at least one second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

having a second structure; where V_(a) in

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

is an n1-dimensional non-zero vector and corresponds to a first group ofantenna ports; 0 in

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

represents an n2-dimensional zero vector and corresponds to a secondgroup of antenna ports; V_(b) in

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

is an n2-dimensional non-zero vector and corresponds to the second groupof antenna ports; and 0 in

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

represents an n1-dimensional zero vector and corresponds to the firstgroup of antenna ports. It should be understood that, the presentinvention is not limited to the case of grouping into only two groups.In an actual application, antenna ports are grouped into more groupsaccording to other factors such as different downtilts or signal qualityor the like. In a specific measurement process, codebooks in the firstcodebook set are traversed, so that a first codebook that best matches atransmission characteristic is determined and used for channeltransmission.

It should be understood that, the structure of the sub-vector in thefirst codebook may be but is not limited to the foregoing firststructure or the second structure. Optionally, locations of sub-vectorsof the zero vector and the non-zero vector in the first codebook may bedifferent. In an embodiment of the present invention, in a case of fourantenna ports, elements in vectors in the first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

having the first structure are represented as

$\begin{bmatrix}V_{a}^{0} \\V_{a}^{1} \\0 \\0\end{bmatrix},$

and elements in vectors in the second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

having the second structure are represented as

$\begin{bmatrix}0 \\0 \\V_{b}^{0} \\V_{b}^{1}\end{bmatrix},$

where V_(a) ⁰ and V_(a) ¹ are elements in the vector V_(a), and V_(b) ⁰and V_(b) ¹ are elements in the vector V_(b). In another embodiment ofthe present invention, when the antenna ports are grouped into twogroups, the first structure may be

$\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix},$

and the second structure may be

$\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix}.$

Likewise, when the antenna groups are grouped into two groups, inanother embodiment of the present invention, the first structure may be

$\begin{bmatrix}V_{a}^{0} \\0 \\0 \\V_{a}^{1}\end{bmatrix},$

and the second structure may be

$\begin{bmatrix}0 \\V_{b}^{0} \\V_{b}^{1} \\0\end{bmatrix}.$

Alternatively, the first codebook set includes at least one of thefollowing four structures: a first structure

$\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix},$

a second structure

$\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix},$

a third structure

$\begin{bmatrix}V_{a}^{0} \\0 \\0 \\V_{a}^{1}\end{bmatrix},$

or a fourth structure

$\begin{bmatrix}0 \\V_{b}^{0} \\V_{b}^{1} \\0\end{bmatrix}.$

V_(a) ⁰ and V_(a) ¹ are elements in the vector V_(a), and Va correspondsto one group of antenna ports. A correspondence is as follows: In thefirst structure, V_(a) ⁰ corresponds to a first antenna port, and V_(a)¹ corresponds to a third antenna port; in the second structure, V_(b) ⁰corresponds to a second antenna port, and V_(b) ¹ corresponds to afourth antenna port; in the third structure, V_(a) ⁰ corresponds to thefirst antenna port, and V_(a) ¹ corresponds to the fourth antenna port;in the fourth structure, V_(b) ⁰ corresponds to the second antenna port,and V_(b) ¹ corresponds to the third antenna port, where V_(a) ⁰ andV_(a) ¹ are elements in the vector V_(a), and V_(b) ⁰ and V_(b) ¹ areelements in the vector V_(b).

When the antenna ports are grouped into three groups, the first codebookset includes at least one of a first structure

$\begin{bmatrix}V_{a} \\0 \\0\end{bmatrix},$

a second structure

$\begin{bmatrix}0 \\V_{b} \\0\end{bmatrix},$

a third structure

$\begin{bmatrix}0 \\0 \\V_{c}\end{bmatrix},$

a fourth structure

$\begin{bmatrix}V_{a} \\0 \\V_{c}\end{bmatrix},$

a fifth structure

$\begin{bmatrix}V_{a} \\V_{b} \\0\end{bmatrix},$

or a sixth structure

$\begin{bmatrix}0 \\V_{b} \\V_{c}\end{bmatrix}.$

Vectors V_(a), V_(b), and V_(c) each correspond to one group of antennaports.

In an embodiment of the present invention, the present inventionprovides a combination of the first structure and the second structurecorresponding to a value of the rank indicator.

Generally, an element in a non-zero vector included in the firstcodebook is in a form of a complex number. For a complex number α·e^(β),α is referred to as an amplitude part, and is a real number, and e^(β)is referred to as a phase part. In still another embodiment of thepresent invention, at least one first codebook meets a first condition.The present invention provides several definitions of the firstcondition that can be implemented. In the present invention, unlessotherwise limited, P, Q, and K are any positive integers.

First Definition of the First Condition:

A vector set formed by all first phase vectors and a discrete Fouriertransform matrix DFT matrix meet a first correspondence that the vectorset formed by the first phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the DFT matrix, wherean element in a P^(th) row and a Q^(th) column in the phase matrix ofthe DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(a) parts of all first sub-vectors

$\quad\begin{bmatrix}V_{a} \\0\end{bmatrix}$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the first phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding first phase vector, where P, Q, and K areany positive integers.

A general expression of the discrete Fourier transform matrix DFT matrixis:

$M_{dft} = {{\frac{1}{\sqrt{N}}\begin{bmatrix}1 & 1 & 1 & 1 & \ldots & 1 \\1 & \omega & \omega^{2} & \omega^{3} & \ldots & \omega^{N - 1} \\1 & \omega^{2} & \omega^{4} & \omega^{6} & \ldots & \omega^{2{({N - 1})}} \\1 & \omega^{3} & \omega^{6} & \omega^{9} & \ldots & \omega^{3{({N - 1})}} \\M & M & M & M & \; & M \\1 & \omega^{N - 1} & \omega^{2{({N - 1})}} & \omega^{3{({N - 1})}} & \ldots & \omega^{{({N - 1})}{({N - 1})}}\end{bmatrix}}.}$

The phase matrix of the DFT matrix is:

$M_{{dft}\; \_ \; {phase}} = {\begin{bmatrix}1 & 1 & 1 & 1 & \ldots & 1 \\1 & \omega & \omega^{2} & \omega^{3} & \ldots & \omega^{N - 1} \\1 & \omega^{2} & \omega^{4} & \omega^{6} & \ldots & \omega^{2{({N - 1})}} \\1 & \omega^{3} & \omega^{6} & \omega^{9} & \ldots & \omega^{3{({N - 1})}} \\M & M & M & M & \; & M \\1 & \omega^{N - 1} & \omega^{2{({N - 1})}} & \omega^{3{({N - 1})}} & \ldots & \omega^{{({N - 1})}{({N - 1})}}\end{bmatrix}.}$

A value of N is an order in a case in which the DFT matrix is a squarematrix. For example, in

$\quad{\begin{bmatrix}V_{a} \\0\end{bmatrix},}$

if Va is four-dimensional, the order of the phase matrix of the DFTmatrix is 4. In an embodiment, a value of ω may be

$\omega = e^{j\frac{2\pi}{N}}$

$M_{{dft}_{—}{phase}_{—}4} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & \omega & \omega^{2} & \omega^{3} \\1 & \omega^{2} & \omega^{4} & \omega^{6} \\1 & \omega^{3} & \omega^{6} & \omega^{9}\end{bmatrix}.}$

For example, when the value of ω is

$e^{j\frac{\; {2\pi}}{32}},$

a form of a fourth-order DFT matrix

$M_{{dft}_{—}{phase}_{—}4_{—}e^{j\frac{2\pi}{32}}}$

is:

$M_{{dft}_{—}{phase}_{—}4_{—}e^{j\frac{2\pi}{32}}} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & e^{j\frac{2\pi}{32}} & e^{2j\frac{2\pi}{32}} & e^{3j\frac{2\pi}{32}} \\1 & e^{2j\frac{2\pi}{32}} & e^{4j\frac{2\pi}{32}} & e^{6j\frac{2\pi}{32}} \\1 & e^{3j\frac{2\pi}{32}} & e^{6j\frac{2\pi}{32}} & e^{9j\frac{2\pi}{32}}\end{bmatrix}.}$

Correspondingly, the set of corresponding columns in the phase matrix ofthe DFT matrix is:

$\left\{ V_{m}^{\prime} \right\} = {\left\{ {\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\e^{j\frac{2\pi}{32}} \\e^{2j\frac{2\pi}{32}} \\e^{3j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{2j\frac{2\pi}{32}} \\e^{4j\frac{2\pi}{32}} \\e^{6j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{3j\frac{2\pi}{32}} \\e^{6j\frac{2\pi}{32}} \\e^{9j\frac{2\pi}{32}}\end{bmatrix}} \right\}.}$

It should be understood that, in the present invention, the phase matrixof the DFT matrix is not necessarily a square matrix. More columns orrows may be selected according to an order. For example, the matrix maybe:

${M^{\prime}}_{{dft}_{—}{phase}_{—}4_{—}e^{j\frac{2\pi}{32}}} = {\begin{bmatrix}1 & 1 & 1 & 1 & 1 \\1 & e^{j\frac{2\pi}{32}} & e^{2j\frac{2\pi}{32}} & e^{3j\frac{2\pi}{32}} & e^{4j\frac{2\pi}{32}} \\1 & e^{2j\frac{2\pi}{32}} & e^{4j\frac{2\pi}{32}} & e^{6j\frac{2\pi}{32}} & e^{8j\frac{2\pi}{32}} \\1 & e^{3j\frac{2\pi}{32}} & e^{6j\frac{2\pi}{32}} & e^{9j\frac{2\pi}{32}} & e^{12j\frac{2\pi}{32}}\end{bmatrix}.}$

The set of corresponding columns in the phase matrix of the DFT matrixis:

$\left\{ V_{m}^{\prime} \right\} = {\left\{ {\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\e^{j\frac{2\pi}{32}} \\e^{2j\frac{2\pi}{32}} \\e^{3j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{2j\frac{2\pi}{32}} \\e^{4j\frac{2\pi}{32}} \\e^{6j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{3j\frac{2\pi}{32}} \\e^{6j\frac{2\pi}{32}} \\e^{9j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{4j\frac{2\pi}{32}} \\e^{8j\frac{2\pi}{32}} \\e^{12j\frac{2\pi}{32}}\end{bmatrix}} \right\}.}$

It should be understood that, a quantity of rows or a quantity ofcolumns selected from the DFT matrix is not limited in the presentinvention. It should be understood that, the quantity of rows should beat least the same as a value of V_(a), and the quantity of columnsshould be at least the same as a quantity of first vectors in acodebook.

Second Definition of the First Condition:

A vector set formed by all second phase vectors and at least one CMPcodebook in a CMP codebook set meet a second correspondence that thevector set formed by the second phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the CMP codebookmatrix, where an element in a P^(th) row and a Q^(th) column in thephase matrix of the CMP codebook matrix is a phase part of an element ina P^(th) row and a Q^(th) column in the CMP codebook matrix, V_(a) partsof all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the second phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding second phase vector, where P, Q, and K areany positive integers, and the CMP codebook refers to a codebook inwhich only one layer in layers corresponding to each port is a non-zeroelement.

In all CMP codebooks, CMP codebooks in which column vectors aretwo-dimensional are:

TABLE 1 Quantity of layers Codebook index v = 1 v = 2 0$\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ 1 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}$ — 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}$ — 3 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}$ — 4 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\0\end{bmatrix}$ — 5 $\frac{1}{\sqrt{2}}\begin{bmatrix}0 \\1\end{bmatrix}$ —

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 1 are:

TABLE 2 Codebook Quantity of layers index v = 1 0-7$\frac{1}{2}\begin{bmatrix}1 \\1 \\1 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\j \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\{- 1} \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\{- j} \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\1 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\j \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\{- 1} \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\{- j} \\{- 1}\end{bmatrix}$  8-15 $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\1 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\j \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\{- 1} \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\{- j} \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\1 \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\j \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\{- 1} \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\{- j} \\1\end{bmatrix}$ 16-23 $\frac{1}{2}\begin{bmatrix}1 \\0 \\1 \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\{- 1} \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\j \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\{- j} \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\{- j}\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 2 are:

TABLE 3 Codebook Quantity of layers index v = 2 0-3$\frac{1}{2}\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}$ 4-7 $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}$  8-11 $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & {- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & {- 1}\end{bmatrix}$ 12-15 $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 1 \\1 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & {- 1} \\1 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 1 \\{- 1} & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & {- 1} \\{- 1} & 0\end{bmatrix}$

For example, when the index in Table 3 is 0, the subset of the set ofcorresponding column vectors in the phase matrix of the correspondingCMP codebook matrix is:

$\left\{ {\begin{bmatrix}e^{0} \\e^{0} \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\e^{0} \\e^{{- j}\frac{\pi}{2}}\end{bmatrix}} \right\}.$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 3 are:

TABLE 4 Code- book Quantity of layers index v = 3 0-3$\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\{- 1} & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\{- 1} & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ 4-7 $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\{- 1} & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\{- 1} & 0 & 0 \\0 & 0 & 1\end{bmatrix}$  8-11 $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1 \\{- 1} & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0 \\{- 1} & 0 & 0\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 4 are:

TABLE 5 Quantity of layers Codebook index v = 4 0$\frac{1}{2}\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}$

Third Definition of the First Condition:

A vector set formed by all third phase vectors is a subset of a setformed by corresponding sub-vectors in a householder transform codebook,where a householder transform expression is W_(n)=I−u_(n)u_(n)^(H)/u_(n) ^(H)u_(n).

V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form a set {V_(m)}, phase parts of all elements ineach sub-vector of the {V_(m)} form the third phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(m)} is a K^(th)element of each corresponding third phase vector.

For example, the third phase vectors are a subset of a set formed byphase parts of W_(index) ^({α) ^(i) ^(}) in a matrix corresponding todifferent quantities of layers and different codebook indexes in Table6. The index corresponds to different codebook indexes. {α_(i)}corresponds to an integer set, and is used to indicate that differentcolumns in W_(index) ^({α) ^(i) ^(}) are selected as third phasevectors. In Table 6, U_(n) is a corresponding U_(n) in the householdertransform, and I is a unit matrix.

It should be understood that, in the present invention, a value of theV_(a) is not limited only to cases or relationships shown in the firstdefinition of the first condition, the second definition of the firstcondition, and the third definition of the first condition. The codebookmay further be a codebook defined for two antennas, four antennas, oreight antennas in LTE.

TABLE 6 Codebook Number of layers ν index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1−1]^(T) W₀ ^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{squareroot over (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁^({12})/{square root over (2)} W₁ ^({123})/{square root over (3)} W₁^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over(2)} W₂ ^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1−j]^(T) W₃ ^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{squareroot over (3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)}−j (1 − j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square rootover (2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1− j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

In still another embodiment of the present invention, at least one firstcodebook meets a second condition. The present invention providesseveral definitions of the second condition that can be implemented.

First Definition of the Second Condition:

A vector set formed by all fourth phase vectors and a discrete Fouriertransform matrix DFT matrix meet a third correspondence that the vectorset formed by the fourth phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the DFT matrix, wherean element in a P^(th) row and a Q^(th) column in the phase matrix ofthe DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(b) parts of all second sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fourth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fourth phase vector.

Second Definition of the Second Condition:

A vector set formed by all fifth phase vectors and at least one CMPcodebook in a CMP codebook set meet a fourth correspondence that thevector set formed by the fifth phase vectors is a subset of a set ofcorresponding column vectors in a phase matrix of the CMP codebookmatrix, where an element in a P^(th) row and a Q^(th) column in thephase matrix of the CMP is a phase part of an element in a P^(th) rowand a Q^(th) column in the CMP codebook matrix, V_(b) parts of allsecond sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the fifth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding fifth phase vector, where P, Q, and K areany positive integers.

Third Definition of the Second Condition:

A vector set formed by all sixth phase vectors is a set formed bycorresponding sub-vectors in a householder transform codebook, whereV_(b) parts of all second sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form a set {V_(n)}, phase parts of all elements ineach sub-vector of the {V_(n)} form the sixth phase vector, and a phasepart of a K^(th) element in each sub-vector of the {V_(n)} is a K^(th)element of each corresponding sixth phase vector.

It should be understood that, in the present invention, a value of theV_(b) is not limited only to cases or relationships shown in the firstdefinition of the second condition, the second definition of the secondcondition, and the third definition of the second condition. The presentinvention requests to protect correspondences according to the secondcondition: a relationship between the fourth phase vectors and differentDFT matrices formed by different parameters, a relationship between thefifth phase vectors and the CMP codebook set, and a relationship betweenthe sixth phase vectors and the householder codebook formed by differentoriginal vectors through householder transforms.

It should be understood that, due to independence, in one codebook, whenthe first codebook meets any definition of the first condition, a secondcodebook may meet any definition of the second condition. For example,in the first codebook, that the vector set formed by the first phasevectors is the subset of the set of corresponding column vectors in thephase matrix of the DFT matrix is met; in the second codebook, that thevector set formed by the fifth phase vectors is the subset of the set ofcorresponding column vectors in the phase matrix of the CMP codebookmatrix, or any combination thereof is met.

In still another embodiment of the present invention, at least one firstcodebook meets a third condition:

In all first amplitude vectors corresponding to {V_(m)}, at least onefirst amplitude vector is different from all second amplitude vectorscorresponding to the {V_(n)}; and/or in all second amplitude vectorscorresponding to the {V_(n)}, at least one second amplitude vector isdifferent from all first amplitude vectors corresponding to the {V_(m)}.V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form the set {V_(m)}, amplitude parts of allelements in each sub-vector of the {V_(m)} form the first amplitudevector, and a phase part of a K^(th) element in each sub-vector of the{V_(m)} is a K^(th) element of each corresponding first amplitudevector; and V_(b) parts of all second sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook form the set {V_(n)}, amplitude parts of allelements in each sub-vector of the {V_(n)} form the second amplitudevector, and an amplitude part of a K^(th) element in each sub-vector ofthe {V_(n)} is a K^(th) element of each corresponding second amplitudevector. In this embodiment, in a sub-vector included in each firstcodebook, an amplitude part of each element corresponds to power of anantenna port. In this embodiment, in a sub-vector included in each firstcodebook, amplitude vectors of each group of antenna ports aredetermined independently according to tilt characteristics of this groupof antenna ports (tilts may be classified into electrical tilts andmechanical tilts; an electrical tilt means that weighted vectors ofmultiple antenna elements corresponding to one antenna port make themultiple antenna elements form a beam pointing to a tilt). For example,all tilts of the first group of antenna ports are 12 degrees, and alltilts of the second group of antenna ports are 3 degrees; it is assumedthat a horizontal plane is 0 degrees and that those downward arepositive tilts. In this case, energies received from the two groups ofantenna ports by the first network device in a location are different.Therefore, independent control may be performed on amplitudes ofcodebooks of the two groups of antenna ports, so that receptionperformance is optimized.

Optionally, FIG. 13 further shows an acquiring unit 404, configured toacquire the first codebook set before the first codebook is selected. Inan embodiment of the present invention, FIG. 14 further shows that thefirst codebook set may be pre-stored in a memory 405, or delivered tothe first network device by the second network device or anotherapparatus.

Optionally, FIG. 15 further shows a second sending unit 406, configuredto send at least one first configuration message to the first networkdevice, where each first configuration message is used to determine asub-vector set of phase parts corresponding to one group of antennaports, and a quantity of the at least one first configuration message isequal to a quantity of groups of the antenna ports; and/or a thirdsending unit 407, configured to send at least one second configurationmessage to the first network device, where each second configurationmessage is used to determine a sub-vector set of amplitude partscorresponding to one group of antenna ports, and a quantity of the atleast one second configuration message is equal to a quantity of groupsof the antenna ports.

The reference signal is further used to indicate the at least one firstconfiguration message, where each first configuration message is used todetermine a sub-vector set of phase parts corresponding to one group ofantenna ports, and a quantity of the at least one first configurationmessage is equal to a quantity of groups of the antenna ports; and/orthe reference signal is further used to indicate the at least one secondconfiguration message, where each second configuration message is usedto determine a sub-vector set of amplitude parts corresponding to onegroup of antenna ports, and a quantity of the at least one secondconfiguration message is equal to a quantity of groups of the antennaports.

In an embodiment, the first configuration message is configured by thesecond network device by using higher layer signaling or dynamicsignaling; and/or the second configuration message is configured by thesecond network device by using higher layer signaling or dynamicsignaling.

In an embodiment, the present invention provides possible cases of acodebook set having the first structure and the second structure. Itshould be understood that, the first codebook that the present inventionrequests to protect may be but is not limited to the followingstructures:

1. the first codebook is one of the following matrices:

${\begin{bmatrix}{V_{a}(i)} \\0\end{bmatrix}\mspace{14mu} {{or}\mspace{14mu}\begin{bmatrix}0 \\{V_{b}\left( i^{\prime} \right)}\end{bmatrix}}},$

where a value of a rank indicator is 1, a non-zero sub-vectorrepresented by V_(a)(x) is a sub-vector in the first vector set {V_(m)}and has a sequence number x, a non-zero sub-vector represented byV_(b)(Y) is a sub-vector in the first vector set {V_(n)} and has asequence number y, 0<i≤N₁, and 0<i′≤N₁, where N₁ represents a quantityof sub-vectors in the {V_(m)}, and N₁′ represents a quantity ofsub-vectors in the {V_(n)}; or

2. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} \\0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},{{or}\mspace{14mu}\begin{bmatrix}0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}},$

where a value of a rank indicator is 2, 0<i≤N₁, 0<i′≤N₁, 0<j N₁, and0<j′≤N₁; or

3. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},{\quad{\begin{bmatrix}0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},{{or}\mspace{14mu}\begin{bmatrix}0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}},}}}}$

where a value of a rank indicator is 3, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, and 0<k′≤N₁; or

4. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},\mspace{140mu} {\quad{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},{\quad{\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\mspace{65mu} \begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},{{or}\mspace{14mu}\begin{bmatrix}0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}},}}}}}}}}$

where a value of a rank indicator is 4, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, and 0<l′≤N₁; or

5. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & 0 & 0\end{bmatrix},\mspace{385mu} \begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(1)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(4)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(1)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},{{or}\begin{bmatrix}0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}},$

where a value of a rank indicator is 5, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, and 0<m′≤N₁; or

6. the first codebook is one of the following matrices:

$\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & 0\end{bmatrix},\mspace{310mu} \begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(5)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(1)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}(i)} & {V_{b}(j)} & 0 & {V_{b}(k)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix},{{or}\mspace{275mu}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}},$

where a value of a rank indicator is 6, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁, and0<n′≤N₁; or

7. the first codebook is one of the following matrices:

${{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}(i)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(4)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}$

${{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 9 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}},$

where a value of a rank indicator is 7, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁,0<n′≤N₁, 0<p≤N₁, and 0<p′≤N₁; or

8. the first codebook is one of the following matrices:

${{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} & {V_{a}(q)} \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}(2)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}(2)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & {V_{a}(p)} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}$

${{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}(i)} & 0 & {V_{b}(j)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0 & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}$

${{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 & {V_{a}(p)} \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & {V_{a}(n)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & {V_{a}(n)} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & {V_{a}(m)} & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(0)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0 & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}$

${{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 & {V_{a}(n)} \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 & {V_{a}(m)} \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & {V_{a}(l)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & {V_{a}(i)} \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)} & 0\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & 0 & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & {V_{a}(l)} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}{V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & {V_{a}(k)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & 0 & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & {V_{a}(i)} & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)}\end{bmatrix}}\begin{bmatrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\{V_{b}\left( i^{\prime} \right)} & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & {V_{b}\left( l^{\prime} \right)} & {V_{b}\left( m^{\prime} \right)} & {V_{b}\left( n^{\prime} \right)} & {V_{b}\left( p^{\prime} \right)} & {V_{b}\left( q^{\prime} \right)}\end{bmatrix}},$

where a value of a rank indicator is 8, 0<i≤N₁, 0<i′≤N₁, 0<j≤N₁,0<j′≤N₁, 0<k≤N₁, 0<k′≤N₁, 0<l≤N₁, 0<l′≤N₁, 0<m≤N₁, 0<m′≤N₁, 0<n≤N₁,0<n′≤N₁, 0<p≤N₁, 0<p′≤N₁, 0<q≤N₁, and 0<q′≤N₁, where for parameters ofi, j, k, l, m, n, p, q, and the like, every two of the sub-vectorscorresponding to the V_(a) parts are unequal, and for parameters of i′,j′, k′, l′, m′, n′, p′, q′, and the like, every two of the sub-vectorscorresponding to the V_(b) parts are unequal.

It should be understood that, in the illustrated possible forms of thefirst codebook included in the first codebook set, i, j, k, l, m, n, p,and q are only for distinguishing locations of different codebookvectors.

Further, in an embodiment of the present invention, V_(a) parts of allfirst sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(K)}, V_(b) parts of allsecond sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(L)}, and thecorresponding {V_(K)} and {V_(L)} in the same first codebook meet afourth condition, where the fourth condition is: phase parts of asub-vector V_(k) in the {V_(k)} form a vector V_(k)′, vectors V_(k)′corresponding to all sub-vectors V_(k) in the {V_(k)} form a set{V_(k)′}, phase parts of a sub-vector V_(L) in the {V_(L)} form a vectorV_(L)′, vectors V_(L)′ corresponding to all sub-vectors V_(L) in the{V_(L)} form a set {V_(L)′}, and {V_(k)′}≠{V_(L)′} holds true. Accordingto concepts of sets, when a quantity of dimensions of the {V_(k)′} and aquantity of dimensions of the {V_(L)′} are unequal, {V_(k)′}≠{V_(L)′}holds true; when a quantity of dimensions of the {V_(k)′} and a quantityof dimensions of the {V_(L)′} are equal, but a quantity of sub-vectorsincluded in the {V_(k)′} and a quantity of sub-vectors included in the{V_(L)′} are unequal, {V_(k)′}≠{V_(L)′} holds true; or when a quantityof dimensions of the {V_(k)′} and a quantity of dimensions of the{V_(L)′} are equal, and a quantity of sub-vectors included in the{V_(k)′} and a quantity of sub-vectors included in the {V_(L)′} areequal, but the sub-vectors included in the {V_(k)′} are different fromthe sub-vectors included in the {V_(L)′}, {V_(k)′}≠{V_(L)′} also holdstrue.

In another embodiment of the present invention, when the value of the RIis greater than 1, V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(M)}, V_(b) parts of allsecond sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in each first codebook form a sub-vector set {V_(N)}, and thecorresponding {V_(M)} and {V_(N)} in the same first codebook meet afifth condition, where the fifth condition is: amplitude parts of asub-vector V_(M) in the {V_(M)} form a vector V_(M)′, vectors V_(M)′corresponding to all sub-vectors V_(M) in the {V_(M)} form a set{V_(M)′}, amplitude parts of a sub-vector V_(N) in the {V_(N)} form avector V_(N)′, vectors V_(N)′ corresponding to all sub-vectors V_(N) inthe {V_(N)} form a set {V_(N)′}, and {V_(M)′}≠{V_(N)′} holds true.According to concepts of sets, when a quantity of dimensions of the{V_(M)′} and a quantity of dimensions of the {V_(N)′} are unequal,{V_(M)′}≠{V_(N)′} holds true; when a quantity of dimensions of the{V_(M)′} and a quantity of dimensions of the {V_(N)′} are equal, but aquantity of sub-vectors included in the {V_(M)′} and a quantity ofsub-vectors included in the {V_(N)′} are unequal, {V_(M)′}≠{V_(N)′}holds true; or when a quantity of dimensions of the {V_(M)′} and aquantity of dimensions of the {V_(N)′} are equal, and a quantity ofsub-vectors included in the {V_(M)′} and a quantity of sub-vectorsincluded in the {V_(N)′} are equal, but the sub-vectors included in the{V_(M)′} are different from the sub-vectors included in the {V_(N)′},{V_(M)′}≠{V_(N)′} also holds true.

In the foregoing embodiment, with the first codebook that makes the{V_(k)′}≠{V_(L)′} and/or {V_(M)′}≠{V_(N)′} relation hold true, flexibleconfigurations of the first structure and the second structure areimplemented, and a codebook is better matched with a channel.

The following provides relationships of amplitude vectors respectivelycorresponding to

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\mspace{14mu} {{{and}\mspace{14mu}\begin{bmatrix}0 \\V_{b}\end{bmatrix}}.}$

A first relationship of amplitude vectors, a second relationship ofamplitude vectors, and a third relationship of amplitude vectors eachprovide a configuration mode of a relationship between elements includedin each sub-vector. The third relationship of amplitude vectors and afourth relationship of amplitude vectors provide relationships betweendifferent codebook vectors in a codebook. The second network device mayconfigure different amplitude vectors according to channel conditions,so that transmission efficiency is higher. The definitions of amplitudevectors are already described, and are not further described herein.

For example, a codebook M₂ in a codebook set is:

$\begin{bmatrix}{a_{1}e^{{jw}_{1}}} & 0 & {b_{1}e^{j\; \theta_{1}}} & {c_{1}e^{j\; \gamma_{1}}} & 0 \\{a_{2}e^{{jw}_{2}}} & 0 & {b_{2}e^{j\; \theta_{2}}} & {c_{2}e^{j\; \gamma_{2}}} & 0 \\{a_{3}e^{{jw}_{3}}} & 0 & {b_{3}e^{j\; \theta_{3}}} & {c_{3}e^{j\; \gamma_{3}}} & 0 \\{a_{4}e^{{jw}_{4}}} & 0 & {b_{4}e^{j\; \theta_{4}}} & {c_{4}e^{j\; \gamma_{4}}} & 0 \\0 & {d_{1}e^{j\; \alpha_{1}}} & 0 & 0 & {0g_{1}e^{j\; \beta_{1}}} \\0 & {d_{2}e^{j\; \alpha_{2}}} & 0 & 0 & {g_{2}e^{j\; \beta_{2}}}\end{bmatrix}.$

If M₂ meets the first relationship of amplitude vectors: at least twoelements in an amplitude vector in V_(a) of each first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are unequal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are unequal, at least two values in a₁, a₂, a₃,and a₄ are unequal; at least two values in b₁, b₂, b₃, and b₄ areunequal; at least two values in c₁, c₂, c₃, and c₄ are unequal; d₁≠d₂;and g₁≠g₂.

If M₂ meets the second relationship of amplitude vectors: at least twoelements in an amplitude vector in V_(a) of each first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are unequal, and all elements in an amplitudevector in V_(b) of each second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are equal, at least two values in a₁, a₂, a₃, anda₄ are unequal; at least two values in b₁, b₂, b₃, and b₄ are unequal;at least two values in c₁, c₂, c₃, and c₄ are unequal; d₁≠d₂; and g₁=g₄.

If M₂ meets the third relationship of amplitude vectors: all elements inan amplitude vector in V_(a) of each first sub-vector

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are equal, and at least two elements in anamplitude vector in V_(b) of each second sub-vector

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are unequal, a₁=a₂=a₃=a₄; b₁=b₂=b₃=b₄;c₁=c₂=c₃=c₄; d₁≠d₂; and g₁≠g₂.

If M₂ meets the fourth relationship of amplitude vectors: at least twoamplitude vectors in a vector set formed by amplitude vectors in V_(a)of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook are different, amplitude vectors in V_(a) of allcorresponding first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in M₂ are

$\begin{bmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4}\end{bmatrix},\begin{bmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4}\end{bmatrix},{{and}\mspace{14mu}\begin{bmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4}\end{bmatrix}},$

where at least two vectors of

$\begin{bmatrix}a_{1} \\a_{2} \\a_{3} \\a_{4}\end{bmatrix},\begin{bmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4}\end{bmatrix},{{and}\mspace{14mu}\begin{bmatrix}c_{1} \\c_{2} \\c_{3} \\c_{4}\end{bmatrix}}$

are different.

A fifth relationship of amplitude vectors is: at least two amplitudevectors in a vector set formed by amplitude vectors in V_(b) of allsecond sub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in the first codebook are different.

In this case, amplitude vectors in V_(b) of all corresponding secondsub-vectors

$\begin{bmatrix}0 \\V_{b}\end{bmatrix}\quad$

in M₂ are

${\begin{bmatrix}d_{1} \\d_{2}\end{bmatrix}\mspace{14mu} {{and}\mspace{14mu}\begin{bmatrix}g_{1} \\g_{2}\end{bmatrix}}},{{{where}\mspace{14mu}\begin{bmatrix}d_{1} \\d_{2}\end{bmatrix}}\mspace{14mu} {{and}\mspace{14mu}\begin{bmatrix}g_{1} \\g_{2}\end{bmatrix}}}$

are unequal.

Optionally, in all the embodiments shown above, the first network deviceis a terminal device UE, and the second network device is a base stationeNB.

FIG. 16 is a flowchart in a system according to the present invention.

501. A second network-side device sends a reference signal to a firstnetwork device, where the reference signal is used to notify the firstnetwork device to perform a measurement to obtain a measurement result.

502. The first network device receives the reference signal, measuresthe reference signal to obtain a measurement result, and selects a firstcodebook from a first codebook set according to the measurement result.

In an embodiment, if a rank is r, the first codebook set C includes nfirst codebooks C(1), C(2), . . . , C(n). A channel matrix H_(Rx×Tx) isobtained by measuring the reference signal, and the rank r is obtainedaccording to the channel matrix H_(Rx×Tx). All the first codebooks C(1)to C(n) whose ranks are r in the first codebook set are traversed. A rowquantity value of the first codebook is Tx, and a column quantity valueof the first codebook is r. Channel quality corresponding to each ofC(1) to C(n) that are included in the first codebook set is calculated.Optionally, the channel quality corresponding to each of C(1) to C(n)may be a channel throughput in each first codebook, or may be a signalto noise ratio of a channel in each first codebook. C(i) is determined,so that the transmission efficiency is highest or optimal. For example,a first codebook corresponding to a maximum channel throughput isselected from all the first codebooks; or a first codebook correspondingto a maximum signal to noise ratio is selected from all the firstcodebooks.

503. The first network-side device sends a codebook index to the secondnetwork device, where the codebook index corresponds to the firstcodebook selected from the first codebook set.

504. The second network-side device receives the codebook index sent bythe first network device, where the codebook index corresponds to thefirst codebook determined in the first codebook set by the first networkdevice.

505. The second network-side device determines, according to thecodebook index, the first codebook determined in the first codebook setby the first network device.

Characteristics of the codebook are already described in the foregoingembodiment, and are not further described herein.

In the following, the present invention provides an embodiment of asub-vector characteristic in the first codebook. Conditions in thisembodiment correspond to the foregoing embodiments.

In an example V₁ of a first codebook:

$V_{1} = {\quad{\begin{bmatrix}0 & \frac{1}{\sqrt{20}} & \frac{1}{\sqrt{20}} & 0 & 0 & \frac{1}{\sqrt{20}} & \frac{1}{\sqrt{20}} & \frac{1}{\sqrt{20}} \\0 & \frac{1}{\sqrt{20}} & {\frac{1}{\sqrt{20}}e^{j\frac{2\pi}{32}}} & 0 & 0 & {\frac{1}{\sqrt{20}}e^{2j\frac{2\pi}{32}}} & {\frac{1}{\sqrt{20}}e^{3j\frac{2\pi}{32}}} & {\frac{1}{\sqrt{20}}e^{4j\frac{2\pi}{32}}} \\0 & \frac{1}{\sqrt{20}} & {\frac{1}{\sqrt{20}}e^{2j\frac{2\pi}{32}}} & 0 & 0 & {\frac{1}{\sqrt{20}}e^{4j\frac{2\pi}{32}}} & {\frac{1}{\sqrt{20}}e^{6j\frac{2\pi}{32}}} & {\frac{1}{\sqrt{20}}e^{8j\frac{2\pi}{32}}} \\0 & \frac{1}{\sqrt{20}} & {\frac{1}{\sqrt{20}}e^{3j\frac{2\pi}{32}}} & 0 & 0 & {\frac{1}{\sqrt{20}}e^{6j\frac{2\pi}{32}}} & {\frac{1}{\sqrt{20}}e^{9j\frac{2\pi}{32}}} & {\frac{1}{\sqrt{20}}e^{12j\frac{2\pi}{32}}} \\\frac{1}{\sqrt{2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\frac{1}{\sqrt{2}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\end{bmatrix},}}$

a met structure is:

$\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & 0 & {V_{a}(k)} & {V_{a}(l)} & {V_{a}(m)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & {V_{b}\left( k^{\prime} \right)} & 0 & 0 & 0\end{bmatrix}.$

A V_(a) part is four-dimensional, and a V_(b) part is alsofour-dimensional. That is, when a quantity of antenna ports in a firstgroup is 4, correspondingly, in a rank 8, there are five correspondingcolumn vectors of W_(x) that meet a first structure. In this case, inthe first codebook, all the sub-vectors W_(x) with V_(a) meeting thefirst structure form a vector set of the first structure, where elementsincluded in the vector set of the first structure are respectively:

${{W_{x}(0)} = \begin{bmatrix}\frac{1}{\sqrt{20}} \\\frac{1}{\sqrt{20}} \\\frac{1}{\sqrt{20}} \\\frac{1}{\sqrt{20}} \\0 \\0 \\0 \\0\end{bmatrix}},{{W_{x}(1)} = \begin{bmatrix}\frac{1}{\sqrt{20}} \\{\frac{1}{\sqrt{20}}e^{j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{2j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{3j\frac{2\pi}{32}}} \\0 \\0 \\0 \\0\end{bmatrix}},{{W_{x}(2)} = \begin{bmatrix}\frac{1}{\sqrt{20}} \\{\frac{1}{\sqrt{20}}e^{2j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{4j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{6j\frac{2\pi}{32}}} \\0 \\0 \\0 \\0\end{bmatrix}},{{W_{x}(3)} = \begin{bmatrix}\frac{1}{\sqrt{20}} \\{\frac{1}{\sqrt{20}}e^{3j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{6j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{9j\frac{2\pi}{32}}} \\0 \\0 \\0 \\0\end{bmatrix}},{{{and}\mspace{14mu} {W_{x}(4)}} = {\begin{bmatrix}\frac{1}{\sqrt{20}} \\{\frac{1}{\sqrt{20}}e^{4j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{8j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{12j\frac{2\pi}{32}}} \\0 \\0 \\0 \\0\end{bmatrix}.}}$

V_(a) parts of all the sub-vectors W_(x) in the vector set of the firststructure form a first vector set {V_(m)}. In this embodiment, thecorresponding {V_(m)} is:

$\left\{ V_{m} \right\} = \left\{ {\begin{bmatrix}\frac{1}{\sqrt{20}} \\\frac{1}{\sqrt{20}} \\\frac{1}{\sqrt{20}} \\\frac{1}{\sqrt{20}}\end{bmatrix},\begin{bmatrix}\frac{1}{\sqrt{20}} \\{\frac{1}{\sqrt{20}}e^{j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{3j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{4j\frac{2\pi}{32}}}\end{bmatrix},{\left. \quad{\begin{bmatrix}\frac{1}{\sqrt{20}} \\{\frac{1}{\sqrt{20}}e^{2j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{4j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{8j\frac{2\pi}{32}}}\end{bmatrix},\begin{bmatrix}\frac{1}{\sqrt{20}} \\{\frac{1}{\sqrt{20}}e^{3j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{6j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{9j\frac{2\pi}{32}}}\end{bmatrix},\begin{bmatrix}\frac{1}{\sqrt{20}} \\{\frac{1}{\sqrt{20}}e^{4j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{8j\frac{2\pi}{32}}} \\{\frac{1}{\sqrt{20}}e^{12j\frac{2\pi}{32}}}\end{bmatrix}} \right\}.}} \right.$

Phase parts of all elements in each sub-vector of the {V_(m)} form acorresponding first phase vector, and a phase part of a K^(th) elementin each sub-vector of the {V_(m)} is a K^(th) element of eachcorresponding first phase vector. A vector set formed by the first phasevectors is

${\left\{ V_{m}^{\prime} \right\} = \left\{ {\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\e^{j\frac{2\pi}{32}} \\e^{3j\frac{2\pi}{32}} \\e^{4j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{2j\frac{2\pi}{32}} \\e^{4j\frac{2\pi}{32}} \\e^{8j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{3j\frac{2\pi}{32}} \\e^{6j\frac{2\pi}{32}} \\e^{9j\frac{2\pi}{32}}\end{bmatrix},\begin{bmatrix}1 \\e^{4j\frac{2\pi}{32}} \\e^{8j\frac{2\pi}{32}} \\e^{12j\frac{2\pi}{32}}\end{bmatrix}} \right\}},$

which is a subset of a set of corresponding column vectors in a phasematrix of a DFT matrix. A phase of a K^(th) element in an M^(th) columnin the {V_(m)} is equal to a K^(th) element in an M^(th) column in the{V_(m)′}. For example, a phase of a fourth element

$\frac{1}{\sqrt{20}}e^{8j\frac{2\pi}{32}}$

in a third column in the {V_(m)} is equal to a fourth element

$e^{8j\frac{2\pi}{32}}$

in a third column in the {V_(m)′}, that is, the matrix V₁ meets: thevector set formed by all the first phase vectors and the discreteFourier transform matrix DFT matrix meet a first correspondence that thevector set formed by the first phase vectors is the subset of the set ofcorresponding column vectors in the phase matrix of the DFT matrix,where an element in a P^(th) row and a Q^(th) column in the phase matrixof the DFT matrix is a phase part of an element in a P^(th) row and aQ^(th) column in the DFT matrix, V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form the set {V_(m)}, the phase parts of all theelements in each sub-vector of the {V_(m)} form the first phase vector,and the phase part of the K^(th) element in each sub-vector of the{V_(m)} is the K^(th) element of each corresponding first phase vector,where P, Q, and K are any positive integers.

In a second embodiment V₂ of a first codebook:

${V_{2} = \begin{bmatrix}0 & 0 & \frac{1}{2} & 0 & 0 \\0 & 0 & {- \frac{1}{2}} & 0 & 0 \\0 & 0 & 0 & 0 & \frac{1}{2} \\0 & 0 & 0 & 0 & {\frac{1}{2}e^{j\frac{\pi}{2}}} \\0 & \frac{1}{2} & 0 & 0 & 0 \\\frac{1}{2} & 0 & 0 & 0 & 0 \\\frac{1}{2} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & \frac{1}{2} & 0\end{bmatrix}},$

a met structure is:

$\begin{bmatrix}0 & {V_{a}(i)} & {V_{a}(j)} & 0 & {V_{a}(k)} \\{V_{b}\left( i^{\prime} \right)} & 0 & 0 & {V_{b}\left( j^{\prime} \right)} & 0\end{bmatrix}.$

A V_(a) part is four-dimensional, and a V_(b) part is alsofour-dimensional. That is, when a quantity of antenna ports in a firstgroup is 4, correspondingly, in a rank 5, there are two correspondingcolumn vectors of the W_(x) that meet a first codebook structure. Inthis case, in the first codebook, all the sub-vectors W_(x) with V_(a)meeting the first structure form a vector set of the first structure,where elements included in the vector set of the first structure arerespectively:

${W_{x}(5)} = {{\begin{bmatrix}\frac{1}{2} \\{- \frac{1}{2}} \\0 \\0 \\0 \\0 \\0 \\0\end{bmatrix}\mspace{14mu} {and}\mspace{14mu} {W_{x}(6)}} = {\begin{bmatrix}0 \\0 \\\frac{1}{2} \\{\frac{1}{2}e^{j\frac{\pi}{2}}} \\0 \\0 \\0 \\0\end{bmatrix}.}}$

V_(a) parts of all the sub-vectors W_(x) in the vector set of the firststructure form a first vector set {V_(m)}. In this embodiment, thecorresponding {V_(m)} is:

$\left\{ V_{m} \right\} = {\left\{ {\begin{bmatrix}\frac{1}{2} \\{- \frac{1}{2}} \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\\frac{1}{2} \\{\frac{1}{2}e^{j\frac{\pi}{2}}}\end{bmatrix}} \right\}.}$

Phase parts of all elements in each sub-vector of the {V_(m)} form acorresponding first phase vector, and a phase part of a K^(th) elementin each sub-vector of the {V_(m)} is a K^(th) element of eachcorresponding first phase vector. A vector set formed by all the firstphase is

${\left\{ V_{m}^{\prime} \right\} = \left\{ {\begin{bmatrix}e^{j\; 0} \\e^{j\; \pi} \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\e^{j\; 0} \\e^{j\frac{\pi}{2}}\end{bmatrix}} \right\}},$

or expressed as:

$\left\{ V_{m}^{\prime} \right\} = {\left\{ {\begin{bmatrix}1 \\{- 1} \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\1 \\j\end{bmatrix}} \right\}.}$

In all CMP codebooks, CMP codebooks in which column vectors aretwo-dimensional are:

TABLE 1 Quantity of layers Codebook index v = 1 v = 2 0$\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ 1 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}$ — 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}$ — 3 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}$ — 4 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\0\end{bmatrix}$ — 5 $\frac{1}{\sqrt{2}}\begin{bmatrix}0 \\1\end{bmatrix}$ —

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 1 are:

TABLE 2 Codebook Quantity of layers index v = 1 0-7$\frac{1}{2}\begin{bmatrix}1 \\1 \\1 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\j \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\{- 1} \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\1 \\{- j} \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\1 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\j \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\{- 1} \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\j \\{- j} \\{- 1}\end{bmatrix}$  8-15 $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\1 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\j \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\{- 1} \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- 1} \\{- j} \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\1 \\{- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\j \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\{- 1} \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\{- j} \\{- j} \\1\end{bmatrix}$ 16-23 $\frac{1}{2}\begin{bmatrix}1 \\0 \\1 \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\{- 1} \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\j \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 \\0 \\{- j} \\0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\{- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 \\1 \\0 \\{- j}\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 2 are:

TABLE 3 Codebook Quantity of layers index v = 2 0-3$\frac{1}{2}\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\1 & 0 \\0 & 1 \\0 & j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- j} & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}$ 4-7 $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & {- j}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & j\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\j & 0 \\0 & 1 \\0 & {- 1}\end{bmatrix}$  8-11 $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\1 & 0 \\0 & {- 1}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\{- 1} & 0 \\0 & {- 1}\end{bmatrix}$ 12-15 $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 1 \\1 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & {- 1} \\1 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 1 \\{- 1} & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 \\0 & 1 \\0 & {- 1} \\{- 1} & 0\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 3 are:

TABLE 4 Code- book Quantity of layers index v = 3 0-3$\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\{- 1} & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\{- 1} & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ 4-7 $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\{- 1} & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\{- 1} & 0 & 0 \\0 & 0 & 1\end{bmatrix}$  8-11 $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1 \\{- 1} & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0 \\1 & 0 & 0\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0 \\{- 1} & 0 & 0\end{bmatrix}$

CMP codebooks in which column vectors are four-dimensional and aquantity of layers is 4 are:

TABLE 5 Quantity of layers Codebook index v = 4 0$\frac{1}{2}\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}$

In this embodiment, in the {V_(m)′}, column vectors arefour-dimensional, and there are two elements in total. In Table 3 inwhich the column vectors are four-dimensional and the quantity of layersis 2, a CMP codebook C_(m) with a codebook index 5 is:

${\frac{1}{2}\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & j\end{bmatrix}},$

and a corresponding phase matrix of the C_(m) is:

$\begin{bmatrix}1 & 0 \\{- 1} & 0 \\0 & 1 \\0 & j\end{bmatrix}.$

The {V_(m)′} and the C_(m) meet a first correspondence: a quantity 2 ofcolumn vectors of {V_(m)′} is equal to a quantity 2 of columns in theCMP codebook; the {V_(m)′} and the C_(m) meet: a vector set

$\begin{bmatrix}1 \\{- 1} \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\1 \\j\end{bmatrix}$

formed by the second phase vectors is a subset of a set of correspondingcolumn vectors in a phase matrix of CMP codebook matrix. Evidently,

$\begin{bmatrix}1 \\{- 1} \\0 \\0\end{bmatrix}\quad$

corresponds to a first column in the phase matrix of the C_(m), and

$\begin{bmatrix}0 \\0 \\1 \\j\end{bmatrix}\quad$

corresponds to a second column in the phase matrix of the C_(m).

That is, the vector set formed by all the second phase vectors and atleast one CMP codebook in a CMP codebook set meet a secondcorrespondence that the vector set formed by the second phase vectors isthe subset of the set of corresponding column vectors in the phasematrix of the CMP codebook matrix, where an element in a P^(th) row anda Q^(th) column in the phase matrix of the CMP codebook matrix is aphase part of an element in a P^(th) row and a Q^(th) column in the CMPcodebook matrix, V_(a) parts of all first sub-vectors

$\begin{bmatrix}V_{a} \\0\end{bmatrix}\quad$

in the first codebook form the set {V_(m)}, the phase parts of all theelements in each sub-vector of the {V_(m)} form the second phase vector,and the phase part of the K^(th) element in each sub-vector of the{V_(m)} is a K^(th) element of each corresponding second phase vector,where P, Q, and K are any positive integers, and the CMP codebook refersto a codebook in which only one layer in layers corresponding to eachport is a non-zero element.

FIG. 17 shows a structure of a general-purpose computer system of theforegoing apparatus.

The computer system may be specifically a processor-based computer, forexample, a general-purpose personal computer (PC), a portable devicesuch as a tablet, or a smartphone.

More specifically, the computer system may include a bus, a processor601, an input device 602, an output device 603, a communicationsinterface 604, and a memory 605. The processor 601, the input device602, the output device 603, the communications interface 604, and thememory 605 are mutually connected by using the bus.

The bus may include a channel, and transfer information betweencomponents of the computer system.

The processor 601 may be a general-purpose processor, for example, ageneral-purpose central processing unit (CPU), a network processor(Network Processor, NP for short), or a microprocessor, or may be anapplication-specific integrated circuit (application-specific integratedcircuit, ASIC), or one or more integrated circuits used for controllingexecution of a program in the solution of the present invention, or maybe a digital signal processor (DSP), an application-specific integratedcircuit (ASIC), a field programmable gate array (FPGA) or any otherprogrammable logic device, a discrete gate or a transistor logic device,or a discrete hardware component.

The memory 605 stores the program for executing the technical solutionof the present invention, and may further store an operating system andother application programs. Specifically, the program may includeprogram code, where the program code includes a computer operationinstruction. More specifically, the memory 605 may be a read-only memory(read-only memory, ROM), another type of static storage device that maystore static information and instructions, a random access memory(random access memory, RAM), another type of dynamic storage device thatmay store information and instructions, a magnetic disk storage, or thelike.

The input device 602 may include an apparatus for receiving data andinformation input by a user, for example, a keyboard, a mouse, a camera,a scanner, a light pen, a voice input apparatus, or a touchscreen.

The output device 603 may include an apparatus that may allow outputtinginformation to the user, for example, a display, a printer, or aspeaker.

The communications interface 604 may include an apparatus that uses anytransceiver, so as to communicate with another device or acommunications network, for example, an Ethernet, a radio access network(RAN), or a wireless local area network (WLAN).

The processor 601 executes the program stored in the memory 605, and isconfigured to implement a method for measuring and feeding back channelinformation according to any embodiment of the present invention and anyapparatus in the embodiment. With descriptions of the foregoingembodiments, a person skilled in the art may clearly understand that thepresent invention may be implemented by hardware, firmware or acombination thereof. When the present invention is implemented bysoftware, the foregoing functions may be stored in a computer-readablemedium or transmitted as one or more instructions or code in thecomputer-readable medium. The computer-readable medium includes acomputer storage medium and a communications medium, where thecommunications medium includes any medium that enables a computerprogram to be transmitted from one place to another. The storage mediummay be any available medium accessible to a computer. The followingprovides an example but does not impose a limitation: Thecomputer-readable medium may include a RAM, a ROM, an EEPROM, a CD-ROM,or another optical disc storage or disk storage medium, or anothermagnetic storage device, or any other medium that can carry or storeexpected program code in a form of an instruction or a data structureand can be accessed by a computer. In addition, any connection may beappropriately defined as a computer-readable medium. For example, ifsoftware is transmitted from a website, a server or another remotesource by using a coaxial cable, an optical fiber/cable, a twisted pair,a digital subscriber line (DSL) or wireless technologies such asinfrared ray, radio and microwave, the coaxial cable, opticalfiber/cable, twisted pair, DSL or wireless technologies such as infraredray, radio and microwave are included in fixation of a medium to whichthey belong. For example, a disk (Disk) and disc (disc) used by thepresent invention includes a compact disc CD, a laser disc, an opticaldisc, a digital versatile disc (DVD), a floppy disk and a Blu-ray disc,where the disk generally copies data by a magnetic means, and the disccopies data optically by a laser means. The foregoing combination shouldalso be included in the protection scope of the computer-readablemedium.

In summary, what is described above is merely exemplary embodiments ofthe technical solutions of the present invention, but is not intended tolimit the protection scope of the present invention. Any modification,equivalent replacement, or improvement made without departing from thespirit and principle of the present invention shall fall within theprotection scope of the present invention.

What is claimed is:
 1. A method for measuring and feeding back channelinformation, the method comprising: determining, by a first networkdevice, a first codebook from a first codebook set, wherein the firstcodebook set comprises at least two first codebooks, wherein asub-vector W_(x) of each first codebook is formed by a zero vector and anon-zero vector, wherein vectors forming the W_(x) are associated withdifferent groups of antenna ports, wherein each first codebook comprisesat least one first sub-vector $\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix}\quad$ and/or at least one second sub-vector$\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix},$ and wherein V_(a) ⁰ and V_(a) ¹ are elements in thevector V_(a), and V_(b) ⁰ and V_(b) ¹ are elements in the vector V_(b);and sending a codebook index to a second network device, wherein thecodebook index is associated with the first codebook selected from thefirst codebook set.
 2. The method according to claim 1, wherein V_(a) isone column of a Discrete Fourier Transform matrix and/or V_(b) is onecolumn of a Discrete Fourier Transform matrix.
 3. A method for measuringand feeding back channel information, the method comprising: sending, bya second network device, a reference signal to a first network device;receiving, by the second network device, a codebook index sent by thefirst network device, wherein the codebook index indicating a firstcodebook of a first code book set, wherein the first codebook setcomprises at least two first codebooks, wherein a sub-vector W_(x) ofeach first codebook is formed by a zero vector and a non-zero vector,wherein vectors forming the W_(x) correspond to different groups ofantenna ports, wherein each first codebook comprises at least one firstsub-vector $\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix}\quad$ and/or at least one second sub-vector$\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix},$ and wherein V_(a) ⁰ and V_(a) ¹ are elements in thevector V_(a), and V_(b) ⁰ and V_(b) ¹ are elements in the vector V_(b);and determining, by the second network device, the first codebookaccording to the codebook index.
 4. The method according to claim 3,wherein V_(a) is one column of a Discrete Fourier Transform matrixand/or V_(b) is one column of a Discrete Fourier Transform matrix.
 5. Aterminal apparatus comprising: a processor configured to determine afirst codebook from a first codebook set, wherein the first codebook setcomprises at least two first codebooks, a sub-vector W_(x) of each firstcodebook is formed by a zero vector and a non-zero vector, whereinvectors forming the W_(x) are associated with different groups ofantenna ports, wherein each first codebook comprises at least one firstsub-vector $\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix}\quad$ and/or at least one second sub-vector$\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix},$ wherein V_(a) ⁰ and V_(a) ¹ are elements in the vectorV_(a), and V_(b) ⁰ and V_(b) ¹ are elements in the vector V_(b); and atransmitter configured to send a codebook index to a second networkdevice, wherein the codebook index is associated with the first codebookselected from the first codebook set.
 6. The apparatus according toclaim 5, wherein V_(a) is one column of a Discrete Fourier Transformmatrix and/or V_(b) is one column of a Discrete Fourier Transformmatrix.
 7. A communications apparatus comprising: a transmitterconfigured to send a reference signal to a first network device; areceiver configured to receive a codebook index sent by the firstnetwork device, wherein the codebook index indicates a first codebook ina first code book set; and a processor configured to determine the firstcodebook according to the codebook index, wherein the first codebook setcomprises at least two first codebooks, wherein a sub-vector W_(x) ofeach first codebook is formed by a zero vector and a non-zero vector,wherein vectors forming the W_(x) correspond to different groups ofantenna ports, wherein each first codebook comprises at least one firstsub-vector $\begin{bmatrix}V_{a}^{0} \\0 \\V_{a}^{1} \\0\end{bmatrix}\quad$ and/or at least one second sub-vector$\begin{bmatrix}0 \\V_{b}^{0} \\0 \\V_{b}^{1}\end{bmatrix},$ and wherein V_(a) ⁰ and V_(a) ¹ are elements in thevector V_(a), and V_(b) ⁰ and V_(b) ¹ are elements in the vector V_(b).8. The apparatus according to claim 7, wherein V_(a) is one column of aDiscrete Fourier Transform matrix and/or V_(b) is one column of aDiscrete Fourier Transform matrix.